Mechanical Puzzles

Jim Storer

Copyright (c) James A. Storer 2018. ## Table Of Contents

Burrs - 23Knot Shaped Three Piece Burrs

Wood Knot - 31

Cross Keys (a.k.a. Three Piece Puzzle) - 32

Knotted Cube - 33

Oskar's Blocks - 34

Shaekel Knot - 35

Cheers - 36Standard Shaped Three Piece Burrs With A Single Trick

Segerblom Knot - 37

Sideways Burr - 38

Sonneveld Three Piece Burr - 39

Triple Play - 40Standard Shaped Three Piece Burrs

Just The Three - 41

3 Piece Burr Yamaosa - 42

Three Open Windows - 43

GigaBurr & GigaBurr II - 44

Cubie Burr & Cubie Burr #2 - 45Burrs With Four or Five Pieces

JA6PB - Just Another 6-Piece Burr - 46

Switch Board Burr - 47

Accordion - 48

Octo Burr - 49Standard Six Piece Burrs

Simple 6-Piece Burr - 50

The Puzzle (a.k.a. Double Cross) - 52

Mikado Block Puzzle - 54

Yamato Block Puzzle - 56

Devil's Knot - 57

Misfit Puzzle - 58

Coffin's Improved Burr - 60

Bill's Baffling Burr - 61

L5 Notchable - 62

Computer's Choice 3-Hole - 63

Computer's Choice 4-Hole - 64

Eight Is Enough - 65

Compter's Choice 5-Hole - 67

The Piston Puzzle - 68

Computer's Choice Unique-10 - 69

L46AA Notchable - 70

Mega Six - 71

Love's Dozen - 72

139 Burr - 73Non-Standard Six Piece Burrs

Twelve Points To Insanity - 74

Dragon Fly - 75

Butterfly - 76

Explode-A-Burr - 77

Programmer's Nightmare - 78

Holey Astigmatism - 79

U-Nam-It Burr - 80

Bill's Ball Bearing Burr - 81

Blind Burr - 82

Luxemburr - 83

Around The Bend - 84

Frantix - 85

Dovetail Burr - 86

Lock Nut - 87

Missing Notch - 88

Three Pieces Puzzle - 89

Tri Again - 90

Zauberflote - 91

Zig-Zag Knot - 92Six Piece Plate Burrs

Chen's Six Board Burr - 93

Chocolate Dip Burr - 94

Gordian Knot - 95

Bent Board Burr #2 - 96Burrs With More Than Six Pieces

Japanese Shape Burrs (a.k.a. Kumiki Puzzles) - 97

Drueke Burrs - Bill's and Marian's Puzzles - 99

Uranus - 100

Miyako Wooden Puzzle - 101

The Aeroplane Block Puzzle - 102

Sydney Harburr Bridge - 103

Bill's Ball Buster - 104

Hectix (a.k.a. Hexsticks, Notched Hexagonal Sticks) - 105

Locked Blocks - 107

Block Puzzle Senior - 108

Satellite Burr - 109

H Burr - 110

Sears Tower - 112

Wausau '81 - 113

Wausau '82 - 114

Wausau 83 - 115

Wausau 84 - 116

Burry Joint - 117

Lassen Risti - 118

Old Oak Of England - 119

Lattice - 120

Quadlock1 - 121

The Pacco Puzzle - 122

Q.E.D. - 123

Miyako 21-Piece - 124

Binary Burr - 125

Visible Burr - 126

SM24 Burr - 130Multi Burrs

Fusion Burr - 139

Four Burr Stick - 140

Four Burrs - 142

Lost Day (a.k.a Eight Burrs) - 143

Berserk BurrCirc - 144Framed Burrs

Oskar's Cube - 146

Two Piece Oddity - 147

Pair Dance - 148

Three Sticks Trapped - 149

Three Trapped Sages - 150

Pandora's Box (a.k.a. Internal Combustion) - 151

Spacemine - 154

Locked Sticks - 155

Two Halves Cage - 156

Constrained Burrs - 157Burr Sets

Simple 6-Piece 6-Solutions Burr Set - 158

Burr Set JCC - 159

CCH Level 1 Key Piece Burr Set - 160

Interlocking Puzzles Burr Set - 162

Interlocking Puzzles Burr Set #2 - 167

Cube Assembly - 170Pieces Made from Unit Size Cubes

Soma Cube - 171

Half Hour - 172

IP Five Piece Cube - 173

Coffin Quartet - 174

Four X - 175

Bedlam Cube - 176

Century Cube - 177Pieces Made from Rectilinear Non-Cubic Shapes

Patio Block - 179

Patio Block MPA - 180

Splitting Headache - 182Pieces Based on Polyhedral Dissections

Quadro Cube - 183

Diagonal Cube - 184Pieces With Interlocking Connections

Cubes And Pegs - 185

Cubes And Pegs Version B - 186

L-Bert Hall - 187

Five Minute Puzzle - 188

Corner Block - 189

Pieces Of Eight - 190

Groovy Cubes - 192

Twenty Cube - 193

Rik's Kiddy Wrapping - 194Manipulation of Connected Cubes

Folding Cubes - 195

Hinged Cubes - 196

Kev's Snake Cubes (a.k.a. Serpent Cubes) - 197

Cubra Cubes - 198

Packing (including 2D Shapes) - 199Checkerboard Puzzles

Checkerboard (a.k.a. All Square Novelty Puzzle, Check-A-Board, ...) - 200

Sectional Checkerboard Puzzle - 201

Chequers (a.k.a. Famous Bug House Puzzle) - 206

The Bug House Puzzle - 208

Famous Baffling Checkerboard Puzzle - 209

XceL Checkerboard Puzzle No. 1 - 210

XceL Checkerboard Puzzle No. 2 - 211

Gyro Checker Board Jig Saw Puzzle - 212

Draught Board Puzzle (a.k.a. Krazee Checkerboard Puzzle, Zebas Puzzle,...) - 213

Adams Idiot's Delight Checkerboard Puzzle - 216

Japanese 19 Piece Checkerboard Puzzle - 217Richter Tangram and the Other 36 Anchor Stone Puzzles

Anchor Puzzle Tangram (a.k.a Caricature, Cut-Up Square ... Richter No. 8) - 218

The Nine (a.k.a. All Nine, Richter No. 1) - 228

Lightning Conductor (a.k.a. Richter No. 2) - 230

Egg Of Columbus (a.k.a. Columbus' Egg, Columbian Puzzle, Richter No. 3) - 234

Patience Prover (a.k.a. Richter No. 4) - 237

Trouble Killer (a.k.a. Richter No. 5) - 240

Heart Puzzle (a.k.a. Richter No. 6) - 243

Kobold (a.k.a. Richter No. 7) - 249

Circular Puzzle (a.k.a. Richter No. 9) - 250

Cross Puzzle (a.k.a. Richter No. 10) - 253

Not Too Hasty (a.k.a. Richter No. 11) - 257

Pythagoras (a.k.a. Richter No. 12) - 260

Tormentor (a.k.a. Richter No. 13) - 266

BeQuiet (a.k.a. Richter No. 14 /3) - 271

Sphinx (a.k.a. Lott's Stone Puzzle, Richter No. 15 / 16) - 274

Magic Egg (a.k.a. Miracle Egg, Richter Anchor Stone Puzzle No. 16 / 17) - 278

Wrath Breaker (a.k.a. Richter No. 17) - 280

Richter Anchor Stone Puzzle No. 23 - 284

Richter Anchor Stone Puzzle No. 26 - 285

Richter Anchor Stone Puzzle No. 27 - 286

Richter Anchor Stone Puzzle No. 28 - 287

Richter Anchor Stone Puzzle No. 29 - 288

Richter Anchor Stone Puzzle No. 30 - 289

Richter Anchor Stone Puzzle No. 35 - 290

Richter Anchor Stone Puzzle No. 36 - 291

Richter Summary - 292Some Other Richter Puzzles and Games

Richter Piccolo Nr. T1 (a.k.a. Richter Picco Nr. T1) - 300

Richter Hamleys - 301

Richter Trench and Zoo Puzzles (a.k.a. Schutzengraben, Zoologischer-Garten) - 302

Richter Star Puzzle - 305

Richter Puzzle Mosaic No. 3 - 308

Richter Meteor 1 - 309

Richter Meteor 6 - 310Other Tangram-Like Puzzles

The Classic Tangram (a.k.a. Richter Anchor Puzzle) - 311

Daddling - 312

Pythagoras - 313

Voodoo - 314

HiHo - 315

Sherlock Holmes - 316

Scrambled Egg - 318

121 Puzzles - 319

ELZZUP - 320

PIC-TUR-ETT - 325

King Tut's Puzzle - 327

HIQU - 328

Shape By Shape - 329Other 2D Puzzles With Polygonal Shapes

Four Piece Square (a.k.a. Magic Square) - 330

Double Square (a.k.a Square Me, Five Block Puzzle, Madagascar Madness) - 331

Missing T (a.k.a. T Puzzle, Magic T, Cut-Up T, Pa's T Puzzle, etc.) - 334

What's Your Score - 337

FPuzzle (theF) - 338

H Puzzle - 339

Pie Without E - 340

Make A Square - 341

Major War Problem - 342Other 2D Packing Puzzles

Checking In - 343

Decoy Puzzle - 344

Batee Baseball - 345

Blockade - 346

Four T Puzzle - 347

Pencil Puzzle - 348

Pearl In The Shell - 349

Czech Farms - 350

Seven - 351Pentominoes

Pentominoes (a.k.a Polyominoes) - 352

Twin Box Pentominoes - 3603D Box Filling

Block Head (a.k.a. Sneaky Squares, Stark Raving Cubes, Square Fit, KUBI) - 361

Three Piece Block Head (a.k.a. The Third Degree) - 362

Coffin's 271A - 363

Log Stacker - 364

Dice Packing Box - 365

Chaotic Cube - 366

Pack It In - 369

Cube Root Blocks - 370

Parcel Post - 371

Bermuda Hexagon - 372

Matching - 3732D Matching

Rubik's Tangle 3x3 (a.k.a Rubik's Mini Tangle) - 374

Rubik's Tangle 3x3 Double Sided - 375

Rubik's Tangle 5x5 - 376

Cluzzelei - 377

Crazy Puzzles - 378

McDonald Land Guzzle - 379

Infants Hospital - The Magic Line - 381

Krazee Links (a.k.a Endless Chain) - 382

Lost Rope - 383

Drive Ya Nuts - 384

Circus Seven (a.k.a. Mind Exerciser) - 385

Circus Puzzler (a.k.a. Color Matcher) - 386

Color Match - 387

Thinkominos - 388

Match The Colors - 389

Triazzle - 390

Bee - 391

Invisible - 392

Snake Pit - 393

Frog Pond - 394

Tool Trouble - 395

Transposer 6 & Bonbons - 396

Transposer Kaboozle - 397

Tantrix Discovery - 398

Tantrix Extreme - 399

Great Gears - 401

Spectra - 402Instant Insanity Family

Instant Insanity (a.k.a Katzenjammer, Great Tantalizer, Face-4, ...) - 404

The Grand Army Puzzle - 417

The Allies Flag Puzzle (a.k.a. The Allied Flags Puzzle) - 418

The Allies Flags Puzzle - 419

Tantalizing Ten - 420

Cuss - 421

Iribako - 422

Drives You Crazy - 423

Boer War Puzzle - 424Other 3D Matching

Bolygok - 426

Double Disaster - 427

Mental Blocks - 428

Disney Cubes - 429

Make A Dice (a.k.a. Spots Puzzle) - 430

Twice Dice - 431

Loony Tunes Blocks - 432

Smarts Pyramid - 433

Smarts PyramidJr - 434

The Rock - 435

Einstein Cube - 436

Rubik Triamid - 437

Other 3D Shape Assembly - 438Convex Polyhedral Shapes

Two Piece Pyramid (a.k.a. Magic Pyramid) - 439

Three Piece Tetrahedron - 440

Four Piece Pyramid, Version 1 - 441

Four Piece Pyramid, Version 2 - 442

Four Piece Tetrahedron - 443

Truncated Tetrahedron - 444

Five Piece Tetrahedron - 445

Truncated Octahedra - 446

Truncated Cubes - 447

Garnet - 448

Y-Knot - 449More Complex Polyhedral Shapes

Three Piece Block - 450

Three Boxy - 451

Three Bunnies - 452

118-X - 453

Three Pairs - 454

Augmented Four Corners - 455

Turnabout - 456

Triumph - 457

Fusion Confusion - 458

Rosebud - 459

Twelve Piece Separation - 460

Crystal Pyramid - 4633D Jig Saw Puzzles

Jig Saw Dog - 464

Wonder Puzzle Block - 465

3x3 Chinese Zigzag - 466

3x4 Chinese Zigzag - 467

Four Piece Jig Saw Puzzle - 468

Wonders Of The World Cube Puzzle - 469Misc. Shape Assembly

Oskar's Matchboxes - 470

Pin-Hole Puzzle (a.k.a Pegged Puzzle) - 471

Wood Star - 472

Saturn Ring - 473

Rubik's Snake - 474

Yin And Yang - 475

Wooden-Do-It (a.k.a. Cigar puzzle) - 476

Gumball Keychains - 478

Hartley's Humpty Dumpty - 479

Almost Impossible Heart - 480

Rubik's Cube Etc. - 481Rubik's Cube - The Two That Started It All

Rubik's 2x2x2 Pocket Cube - 482

Rubik's 3x3x3 Cube - 493More Rubik's Type Cubes

Rubik1x2x2 - 507

Rubik 1x2x5 - 508

Rubik 1x2x9 - 509

Rubik 1x2x13 (a.k.a. Unlucky Twist) - 510

Rubik 1x3x3 Floppy Cube - 511

Rubik1x3x3 Floppy Mirror Cube (a.k.a. Magic Floppy Cube) - 512

Rubik1x3x3 Scramble Cube - 513

Rubik 2x2x2 Bandaged - 514

Rubik 2x2x2 Double Bandaged - 515

Rubik 2x2x2 Nested (a.k.a. Rubik 2x2x2 Super Square) - 516

Rubik 2x2x2 Cubes Fused - 517

Rubik 2x2x3 Tower Cube (a.k.a. Slim Tower, Franken Tower) - 518

Rubik 2x2x4 Tower - 519

Rubik 2x2x4 Nested (a.k.a. Rubik 2x2x4 Super Square) - 520

Rubik 2x2x23 (a.k.a. Overlap Cube) - 521

Rubik 2x3x3 Domino - 522

Rubik2x3x3 Layered - 523

Rubik 2x3x4 - 524

Rubik 2x4x4 (a.k.a. WitEden 2x4x4) - 525

Rubik 3x3x3 Mirror Cube (a.k.a. Mirror Block, Yong Jun Cube) - 526

Rubik3x3x3 Fisher Cube (a.k.a. Square King) - 527

Rubik 3x3x3 Void Cube (a.k.a. Holey Cube) - 528

Rubik 3x3x3 Edges Only (a.k.a. Cornerless Void Cub) - 530

Rubik's 3x3x3 Fourth Dimension - 531

Rubik 3x3x3 Layered - 532

Rubik's 3x3x3 Perpetual Calendar - 533

Rubik 3x3x3 Bandaged (a.k.a. Bicube) - 534

Rubik 3x3x3 Patched (a.k.a. Fused Cube) - 535

Rubik 3x3x3 Brick (a.k.a Brick Cube) - 536

Rubik 3x3x3 Latch Cube - 537

Rubik 3x3x3 Constrained (a.k.a. TomZ / Tom's Constrained Cube) - 538

Rubik 3x3x4 - 539

Rubik 3x3x5 - 540

Rubik 3x3x5 X - 541

Rubik 3x3x5 Cross - 542

Rubik 3x3x9 - 543

Rubik 3x3x9RoadBlock - 544

Rubik 3x4x5 - 545

Rubik 4x4x4 - 546

Rubik 4x4x4 Patched - 554

Rubik 4x4x4 Brick - 555

Rubik 4x4x5 - 556

Rubik 4x4x6 (a.k.a. TomZ 4x4x6 Cuboid) - 557

Rubik 5x5x5 - 558

Rubik 6x6x6 (a.k.a. V-Cube 6x6x6) - 561

Rubik 7x7x7 (a.k.a. V-Cube 7x7x7) - 562

Large Rubik Cubes - 563

Huge Rubik Cubes - 564Camouflage Cubes / Evil Cuboids

Camouflage Cube 3x3x3 - 565

Camouflage Cube 3x4x4 - 566

Evil Cuboid 2x3x4 - 567

Evil Cuboid 3x3x3 - 568

Evil Cuboid 3x4x5 - 569Crazy Cubes

Crazy Cube 2x3x3 - 570

Crazy Cube 3x3x3 - 571

Crazy Cube 3x3x7 (a.k.a. WitEden Super Magic Cube) - 572

Crazy Cube 4x4x4 - 573

Crazy Cube 4x4x4 Two - 574Gear Cubes

Geared 1x1x4 - 575

Geared 2x2x2 - 576

Geared Mixup - 577

Gear Cube - 578

Gear Cube Extreme - 579

Timur Gear Skewb - 580

Gear Shift - 581Other Rectangular Shapes

Mixup Cube - 582

Ghost Cube - 583

Pocket Cube - 584

Axel Cube - 585

Skewb - 586

Holey Skewb (a.k.a. Void Skewb) - 588

Golden Cube - 589

Dino Cube (a.k.a. Dinosaur Cube) - 590

Blue Magic (a.k.a. Black Flower Cube, Star Cube, Rex Cube) - 591

Mosaic Cube - 592

Square 1 (a.k.a. Super Cubix, Cube 21) - 593

Helicopter Cube - 601

Curvy Copter - 602Pyrmid and Diamond Like Shapes

Pyraminx - 603

Pyraminx Duo - 607

Pyraminx Diamond - 608

Jing's Pyraminx (a.k.a. Rounded Halpern-Meier Pyramid) - 609

Crazy Pyraminx (a.k.a. Crazy Tetrahedron Plus) - 610

Gear Pyraminx - 611

Gear Pyraminx2 (a.k.a. Gear Mastermorphix) - 612

Tetraminx - 613

Professor Pyraminx - 614

Vulcano - 615

Megaminx (a.k.a. Supernova) - 616

Holey Megaminx - 617

Crazy Megaminx - 618

Gear Minx - 619

Kilominx (a.k.a. Flowerminx) - 620

Master Kilominx - 621

Gigaminx - 622

Teraminx - 623

Gear Change - 624

Pyraminx Crystal - 625

Helicopter Dodecahedron - 626

Skewb Diamond - 627

Super Skewb Diamond (a.k.a. Diamond Octahedron) - 628

Skewb Ultimate - 629

Skewb Kite - 630

Skewb Fourteen - 631

Pyrastar - 632

Pyramorphix (a.k.a Figurenmatch, Distortion Demon Square) - 633

Starburst (a.k.a. Star of David, Sterns Puzzle) - 634

Mastermorphix (a.k.a. Master Pyramorphinx) - 635

Dinomorphix - 636

Pillow Cube (a.k.a. Cushion Cube) - 637

Enhanced Pillow Cube (a.k.a. Polish Cushion) - 638

Confused Pillow Cube - 639

Hungarian Diamond - 640

Rhombi Diamond (a.k.a. Diamond Style Puzzler) - 641

Octahedron (a.k.a. Magic Octahedron) - 643

Full Octahedron - 644

Flowered Jewel (a.k.a Jewel Puzzler, Christopher's Magic Jewel, ...) - 645

Gear Octahedron (a.k.a. Timur Gear Corner Turning Octahedron) - 646Disc and UFO Shapes

Rubik's Cheese - 647

Rubik UFO - 648

UFO Cheese - 649

Rubik Cheese Cake - 650

Puck Puzzle (a.k.a Hockey Puck Puzzle) - 651

Saturn - 652

Hungarian UFO (a.k.a. Varia Disk) - 653

Tricky Disky (a.k.a. Tricky Disk, Mind Trapper) - 654

Smart Alex (a.k.a Alpa-2-Go) - 655

Netblock UFO / Sando Ring (a.k.a. King Ring) - 656

Octo (a.k.a. Meeting Colors, Disco Puzzle) - 657

Gerdig UFO - 658

Brain Ball - 659Sphere Shapes

Rubik 2x2x2 K-Ball - 660

Rubik 3x3x3 Ball - 661

Rubik 3x3x3 Apple - 662

Gear Ball - 663

Master Ball (a.k.a. Duo Master, Geo Master) - 664

Skewb Puzzle Ball (a.k.a Creative Puzzle Ball) - 667

Impossiball - 669

Dogic - 670Other Shapes

Rubik House (a.k.a. Eight Planets Bermuda Cube) - 671

Time Machine - 672

Rubik Barrel - 673

Cuboctahedron - 674

Rainbow Cube - 675

Rainbow Nautilus - 676

Pentahedron - 677

Pentahedron 5 Layer - 678

Crazy Pentahedron - 679

Dino Star - 681

Alexander's Star - 682

Platypus - 683

Skewb Egg (a.k.a. Golden Egg, Silver Egg, etc.) - 684

Brain Twist - 685

Roundy - 686

Other 3D Manipulation - 687Panel Puzzles

Rubik Mini Magic Panels (a.k.a Rubik Magic Junior) - 688

Rubik's Magic Panels - 693

Rubik Magic Panels Create The Cube - 701

Rubik's Master Magic Panels - 703

Rubik Magic Cross Panels - 705

Rubik Super Magic Panels - 706Towers Of Moving Balls Or Tiles

Whip-It Towers (a.k.a. Genius Puzzle) - 708

Varikon Towers - 709

Whip-It Ball - 711

Babylon Towers - 712

Calendar Bank - 713

Thai Tower (a.k.a. Clever Toys Tower) - 714

Numbers Barrel - 715

Missing Link - 716

Reduced Missing Link - 718

Extended Missing Link - 719

Doubled Missing Link - 720

Mini Missing Link - 722Other Puzzles With Moving Balls or Tiles

Magic Rainbow Ball - 723

Hungarian Globe (a.k.a. Equator Ball, Magic Sphere, IQ Ball) - 724

Bolaris - 726

Magic Sphere - 727

Touchdown - 728

Twister (a.k.a. Wooden Screwball, Clever Toys Natural) - 729

Atomic Chaos (a.k.a. Kaos) - 730

Entrapment - 731

Pakovalec (a.k.a. Stupid Cylinder) - 732

Ten Billion Barrel (a.k.a. Billion Barrel, Tumbler Puzzle) - 733

Russian Revolver (a.k.a. Russian Flower, Russian UFO, Soviet UFO) - 734

Back Spin (a.k.a. Loophole) - 735

Sliding Piece Can Puzzle - 736

Sliding Piece Can Puzzle - 737

Brain Racker - 738

The Orb (a.k.a. Orb-It, l'ORBS) - 739

Rubik's Shells - 740

Astrolabacus - 741Movement of Pieces by Tilting or Pushing

Varikon Box 2x2x2 - 742

Varikon Box 3x3x3 - 743

Inversion - 744

Peter's Black Hole / Vadasz Cage (a.k.a. Inside Out, Magic Jack, IQ Cube) - 746

Mad Marbles - 747

Dice Box - 748

Clark's Cube - 749

Pionir Box (a.k.a. Pionir Cube) - 750

Rubik Dice - 751Movement of Discs and Rings

Towers Of Hanoi (a.k.a. Pyramid Piling Puzzle, Rainbow Puzzle, Brahma Puzzle) - 752

Chinese Rings (a.k.a. Cardan's Rings, Baguenaudier) - 755

Spinout - 759

Hexadecimal Puzzle - 760

WanderRings - 764

Panex - 766Manipulation Of Positioned Balls, Levers, Buttons, Etc.

Cmetrick - 767

Cmetrick Too (Hard) - 768

Planets - 769

SaturnLD - 770

Orbik - 773

Rolling Cubes - 774

Cross Teaser - 775

Rubik's Clock - 776

Cerebral Rings Puzzler - 778

Simultaneous Maze - 779Misc.

Wisdom Ball (a.k.a. Mind Twister) - 780

SpongeBob PuzzlePants (a.k.a. SpongeBob Cube) - 781

Flip Side - 782

Kabalabda - 783

Rubik's Rabbits (a.k.a. Rubik's Hat) - 784

Enigma - 785

Brain Puzzler - 786

Sliding Pieces and Other 2D Manipulation - 787Square Pieces

Fifteen Puzzle - 788

Unocando - 836

Sixteen Puzzle - 837

Eight Puzzle (a.k.a. Super Solitaire) - 838

Nine Puzzle - 839

Ditho (a.k.a. Fourteen Puzzle) - 842

Great Fifty Puzzle - 845

Panama Canal Puzzle - 846

Moving Day (a.k.a. a.k.a. 5-Block Puzzle, Lodging House Difficulty) - 850

Bull's-Eye (a.k.a. Bullseye, Target, Zot) - 851

Good Luck - 857

Twenty - 858

Double Trouble Puzzle - 859

Twenty Seven - 860

Scrabble Pocket Puzzle - 862

Thirty One (a.k.a. Jumble) - 863

RO-LET - 865

Cornell Crossword Puzzle - 866

SKOR - 867

ScribeO - 868

LINGO - 869

Missionary Puzzle - 873

Mystic - 874Square Pieces With Obstacles

Grandpa's Car (a.k.a. Slide-Blocked Sliding Block) - 875

Time Puzzle - 876

Work Or Golf (a.k.a. Motor Garage Puzzle, Parka Car, Sputnik, E Peg Puzzle) - 879

Honor And Glory (a.k.a. Black And White) - 882

One Fish Another Fish - 8841x2 Pieces and (in most cases) 1x1 pieces

Get My Goat (a.k.a. Kapture The Kron Prinz, Boogie Man, Center Point, ...) - 885

Line Up The Quinties - 891

Johnson City Puzzle - 893

Four Suits 2 - 895

Puzzle Contrast - 896

Sliding Arrow Through The Bottle Puzzle - 897

Slidem WWII Puzzles - 898

Monarch - 902

Sliding Chess Mate 36 - 903

Straight Arrow - 904Dad's Puzzler Family - 4x5 Trays and Multiple Shapes Rectangular Pieces

Dad's Puzzler (a.k.a. Moving Puzzle, Tit-Bits Teaser 1, Pennant Puzzle, ...) - 905

Dads Puzzler - Humdinger Version - 940

Dad's Puzzler - Exchange Version / Infants' Hospital - 947

Quzzle And Quzzle Killer - 954

Nine Block - 958

Red Donkey, with Simple TJ, Century, Super Century (a.k.a. L'Ane Rouge, ...) - 961

Traffic Jam / Let Me Through - 971

Century and Super-Century - 976

Grand Master With Century And A Half and Little House - 982

Ushi And Ushi-Flipped - 986

Hole In One With Royal Out and King Out - 989

Fence The Cow - 992

Dad's Puzzle Family Set With Fujiwara 15/22/25 and Super Compo - 994Dad's Puzzler Family With Obstacles and Non-Rectangular Pieces

D209 - 999

Super Dries - 1000Beyond Dad's Puzzler Family

Sunbeams Rainbow Puzzle - 1001

Infants Hospital Puzzle (a.k.a. Infants Progress Puzzle) - 1002

Trans-Atlantic (a.k.a. Ten Block Puzzle, Traffic Cop Tangle) - 1004

Happy Couple (with Ten Block and The Hughes Puzzle) - 1006

Flying Puzzle (a.k.a. Starry Puzzler, Tit-Bits Teaser No. 2, Ching Foo, ...) - 1012

Technocracy - 1022

George Washington Puzzle - 1023

Presidential Puzzle - 1026

Tit Bits Teaser No. 5 - 1028

Century Of Progress (a.k.a. South Pole Expedition) - 1033

Sliding Block Puzzle (a.k.a. Fifteen Block Puzzle, 1-2-3 Puzzle, ...) - 1035

Slide A While & Model Garage - 1040

Tokyo Parking / Rush Hour - 1045

Adam & Eve (a.k.a. Comic Scramble Game) - 1049

RunAway II - 1051

Neo Pink And Blue - 1053Further Beyond Dad's Puzzler Family - Non-Rectangular Shapes

Ma's Puzzle (a.k.a. Spirit of '76, Wooden Puzzle, Rectangle Puzzle) - 1056

Dad's and Ma's Stumbling Blocks (a.k.a. Dad's Puzzler + Ma's Puzzle) - 1063

Mini Ma - 1064

Traffic Jam Puzzle (a.k.a. Tit-Bits Teaser No. 4) - 1065

Triple Tango - 1072

Clouds And Sheep - 1073

Slider (a.k.a. Hole In One) - 1074

Heart-In - 1075

Soap - 1076

Block Ten - 1077

Stumbling Block - 1083

I Want You - 1085

Neo Black And White - 1087

Kuroko And Dairu - 1092

Dinosaur Egg (a.k.a. Egg Puzzle) - 1093

Solo - 1094

Angel And Satan - 1095

Dog And Cat - 1096

Two Sliding Squares - 1097Sliding Pieces Non-Standard Movement - layers, capture movement, rotations, etc.

Get My Sheep - 1098

Two Eggs - 1100

Sliding Cross - 1110

Football Match - 1119

Sliding Three - 1122

Neo Slide-9 - 1123

RunAway - 1125

Trap - 1127

Tricky - 1135

Two Dogs - 1143

Stacking Cups - 1146

Train Puzzle - 1153

Dustin Puzzle - 1154

Who's The Boss - 1155

Easy - 1161

Easy 1989 - 1163Movement of Buttons, Balls, Numbers, etc.

New Fifteen Puzzle - 1165

Perplexity Puzzles (Perplexity, Automobile, This is Jonah, Panama Canal) - 1166

One To Ten - 1167

Good Luck Railroad Puzzle Game - 1168

Rotos - 1169

Puzzler Novice / Challenge / Avenger (a.k.a. Turnstile, Twinspin, ...) - 1170

Rotascope (a.k.a. Taquinoscope) - 1171

Hungarian Rings - 1173

Hungarian Rings Triple - 1174

Hungarian Rings Quad - 1175

Hungarian Olympic Rings - 1176

One Circle Two Circles - 1177

Billiards - 1178

Billiards 9-Ball - 1179

Flower - 1180

Trio - 1181

Trio 2 - 1182

Butterfly - 1183

Subway Shuffle - 1184Movement of Tokens

Eight Peg Puzzle - 1190

TeeZ / Brain Buster - 1191

Peg Puzzle - 1192

Hopper (a.k.a. Downsize) - 1193Mechanically Assisted Sliding Pieces

Top Spin / No. Crunch - 1195

Line Art - 1196

Colour Match - 1197

Magic Cross (a.k.a. Zauberkreuz) - 1198

Rubik's XV (a.k.a. Rubik's Fifteen) - 1199

Tsukuda's Square (a.k.a. It, 4x4 Four By Four Puzzle) - 1200

Uriblock (a.k.a. Mix Box) - 1201

Trillion - 1202

Port To Port And Triple Cross - 1204

Switch Back - 1208

SwissMad - 1209

Modern Times - 1210

Mad Triad Challenge (Twisting Tri-Side Puzzle) - 1211

Mad Triad Handy (Twisting Tri-Side Puzzle) - 1212

La Cerradura Doble - 1213

Elemental Neon - 1214

Fluorine - 1216

SF PP STAR 29 - 1217

String and Wire Puzzles - 1218Move or Remove a Ring

Horse Shoes - 1219

Ball And Ring (a.k.a. Ball And Chain) - 1220

Moving Rings (a.k.a. Moving Beads, Tiger Cross, Wizzard Wedding Ring) - 1221

Wits End - 1222

Single Loop Wit's End - 1224

Loop Trap - 1225

Parallel Dimension - 1226Disengage Two Pieces

Nails - 1227

Wire U's - 1228

Wire P's - 1229

Wire Heart - 1230

Cast Ring - 1231

Vortex - 1232

Simple Knot 47091 - 1233

EZ Atom 47092 - 1234

Lucky Clover - 1235Misc.

Rod and Loop - 1236

Hide The Knots - 1237

Other Puzzles - 1238Mechanicl Challenges

TakitaparT (a.k.a Take It Apart) - 1239

Double Puzzle - 1240

Rook Puzzle - 1241

Bolt And Ball - 1242

Spark Plug Puzzle (a.k.a. Bougie, Get Charged) - 1243

Cage Puzzle - 1244

Drive The USA - 1245

Screwball - 1246

Magic Chalice - 1247Dexterity Puzzles

Abercrombie & Fitch Dexterity Puzzles - 1248

A Ward In The Infant's Hospital (a.k.a. The Little Patients Puzzle) - 1249

ElsieCow - 1250

Reiss Style 393 - 1251

Crazy Maze - 1252

Metro - 1253

Perplexus - 1254Brain Teasers

What's Your Age - 1255Jigsaw Puzzles

Infants Hospital Jigsaw Puzzle - 1256Puzzle Boxes

Parrot Box - 1257

Spin Box - 1258

Coffin's Double Play X-48 - 1259

Stickman Fulcrum Box - 1260

Pirate's Wallet Box (a.k.a. Stickman No. 27) - 1261

Stickman Grandfather Clock - 1270

Games - 1276

Goblet - 1277

Quixo - 1280

Quarto - 1281

Othello - 1282

Nine Mens Morris (a.k.a. Mill, Muhle, Merelles / Merilles, Mulino) - 1283

Tablut - 1285

Senet - 1287

Nannon (a.k.a. Nano Backgammon) - 1291

Make Numbers - 1292

Books - 1293Hoffmann Related Books

Hoffmann's Puzzles Old and New (1893) - 1294

Hordern's Edition Of The Hoffmann Book (1993) - 1300

Het Puzzle-Boek (1900) - 1301

Hoffmann Posthumous Books (1925) - 1302

Hoffmann's Best Math Book (2007) - 1303

Hoffmann Patience Games Book (1892) - 1304

Hoffmann's Magic Trilogy Books (1920) - 1305

Hoffmann Study Book (1977) - 1306Other Books from Before 1960

Robert Merry's Books Of Puzzles 1-3 (1866) - 1307

Excursions Into Puzzledom (1879) - 1309

Everybody's Puzzle Book (1890) - 1310

Richter Company U.S. Brochure (early 1900's) - 1311

New Book Of 200 Puzzles (1908) - 1318

Dudeney Books (1920's) - 1319

Dudeney Posthumous Books - 1320

Sam Loyd's Cyclopedia Of Puzzles (1914) - 1321

Sam Loyd and His Puzzles (1928) - 1322

Wyatt's 1928 and 1946 Books - 1323

Johnson Smith Catalog (reprinted from 1929) - 1324

Hirschberg Book (1930) - 1325

I-X-L Puzzle Book (1938) - 1326

Filipiak Book (1942) - 1327

Everythings A Puzzle (1953) - 1328Books 1960 - 1999

Bell's History of Board Games (1960) - 1329

Murray's History of Board Games (1978) - 1330

Delft And Botermans Book (1978) - 1331

Winning Ways Books (1982) - 1332

Hordern's Sliding Puzzle Book (1986) - 1333

Slocum and Botermans Books (1986) - 1334

Cutler's 6-Piece Burr Books (1986) - 1335

The Mathematics Of Games (1989) - 1336

Coffin's Book On Polyhedral Dissections (1990) - 1337

Coffin's Puzzle Craft Books (1992) - 1338

The Puzzle Archade (1996) - 1339

Gabarchuk's Sliding Block Puzzle Book (1996) - 1340

Frederickson's Dissections Book (1997) - 1341

G4G Tributes To Martin Gardner (1999) - 1342Books 2000 - present

The Follette Puzzle Design Book (2001) - 1343

The Tangram Book (2003) - 1344

Haubrich's Checkerboard Puzzles (2005) - 1345

The Fifteen Book (2006) - 1346

A Visual History of The S.S. Adams Co. (2006) - 1347

The Self and Lensch Puzzle Design Book (2006) - 1348

Boardman's Puzzle Projects Book (2007) - 1349

The Cube Book (2009) - 1350

Hess Mathlete Book (2009) - 1351

Diaconis and Graham Book (2012) - 1352

Stickman Book (2012) - 1353

The Anchor Puzzle Book (2012) - 1355

Coffin's AP-ART Book - 1357--- 23 --- Burrs

Pieces are formed by removing unit cubes from rectilinear solid pieces. A burr isnotchableif it can be made with just straight cuts. Some burrs have a "key" piece that slides out. More complex ones have a number of internal voids (calledholes), where removing the first piece may require sliding several pieces. Anassemblyof a burr is a solved shape. An assembly is asolutionif it can be achieved by starting with the pieces apart and making legal moves. Thelevel of a solutionis the minimum number of moves required to remove the first piece (or separate the puzzle into two parts). Thelevelof a burr is the lowest level of its solutions. Note that to compute level, we useCutler'sdefinition, where the movement of several pieces together, or the consecutive movement of pieces in the same direction, counts as a single "move". Burr level can be expressed with more than one number; e.g., 3.7.2 means 3 moves to remove the first piece, 7 moves to remove the second piece, and 2 moves to remove the third piece.--- 24 --- Standard Six Piece Burrs

The most well known burr is the standard 6 piece burr, with 2 x 2 x 6 unit pieces (or sometimes 2 x 2 x 8). For example, the figure above showsCoffin's Improved Burr, which requires 3 moves to remove the first piece (letters show how pieces fit, numbers indicate an order in which they can be disassembled).

The number of holes in a standard 6-piece burr:

- Volume of six solid pieces = 6 x 24 = 144 (or 192 for 2x2x8 pieces).

- Volume of a solid burr = 24+24+16+16+12+12 = 104 (or 152 for 2x2x8 pieces).

- Volume difference = 40.

- Holes = (total number of unit cubes removed from the six pieces) - 40.
Standard 6-piece burr records, from the computer work of Bill Cutler:

- Highest level for unique solution with 3 holes = 7.
- Highest level for unique solution with 4 holes = 8.
- Highest level for unique solution with 5 holes = 9.
- Highest level with a unique solution (uses 7 holes) = 10.
- There are no standard 6-piece burrs of level 11.
- Highest possible level (its the only one, but has non-unique solution) = 12.
- Highest level for unique notchable (has 7 holes) = 5.
- Highest level for notchable with non-unique solution = 10.
--- 25 --- Interesting Issues For BurrsQuestions and generalizations for 6-piece burrs:

- Highest level when fractional moves may be made.

- Highest level when rotations may be made.

- Non-rectangular cuts.

- Solutions that have exposed holes.

- Ball bearings inside.

- Solutions where the additional moves to remove the second piece require more moves than the first.

- Etc.
Other Types of Burrs:

Non-standard 6-piece burrs have six pieces but don't adhere to standard construction rules. Burrs in the theme of the standard 6-piece burrs but with more pieces can be very hard, and more pieces combined with non-standard types of constructions can derail approaches that you have worked out for standard constructions. Finally, burrs with fewer than six pieces can be quite fun. The most well known are 3 piece "knots" that fit together in a simple but not at first apparent way. Some three piece knot variations require unusual twists or diagonal motions as well. Burrs in the theme of the standard 6-piece burrs with as few as 3 pieces can be quite difficult (e.g., the Cuter Level 8 GigaBurr).--- 26 --- Burr HistoryThe basic idea of a burr seems quite old. The 1893Hoffman bookpresents a wood knot as "Cross Keys" and a 6-piece burr as "The Nut". The 1929Johnson and Smith Catalog, on pages 254-255, shows a 6-piece burr, a two burr stick, and related wood puzzles. ThePuzzlers' Tribute book, on page 260 cites a 6-piece burr called theDevil's Hoofand a 24-piece burr called theLarge Devil's Hoofin a Catel's catalogue of 1785, and credits David Singmaster as having found an example of a 6-piece burr in a 1733 Spanish book by Pablo Minguet E. Irol; also, on page 262 it credits the Mikado Puzzle as shown in the 1915 C. J. Felsman Catalogue.

The Slocum and Botermans New Book of Puzzles on page 52 discusses the Spears Puzzle knots manufactured in Bavaria in 1910 and marketed in England; it is also mentioned that six piece burrs appeared in Bestelmeier's 1803 Toy Catalog.--- 27 --- Classic BurrsThe 1942 Filipiak book has a substantial discussion of burr puzzles; here are figures it shows of a 3-piece wooden knot, a 6-piece burr, and a 6-piece burr set:

--- 28 --- Burr PatentsThere have been many burr patents; for example, here are the figures from the 1890 Altekruse and 1917 Brown patents:

--- 29 --- Some Burr PatentsChandler Patent, from: www.uspto.gov - patent no. 393,816

Altekruse Patent, from: www.uspto.gov - patent no. 430,502

Porter Patent, from: www.uspto.gov - patent no. 524,212

Nelson Patent, from: www.uspto.gov - patent no. 588,705

Ford Patent, from: www.uspto.gov - patent no. 779,121

Curtis Patent, from: www.uspto.gov - patent no. 781,050

Erickson Patent, from: www.uspto.gov - patent no. 985,253

Banic Patent, from: www.uspto.gov - patent no. 1,099,159

Brown Patent, from: www.uspto.gov - patent no. 1,225,760

Keiser Patent, from: www.uspto.gov - patent no. 1,261,242

Senyk Patent, from: www.uspto.gov - patent no. 1,350,039

Schenk Patent, from: www.uspto.gov - patent no. 1,455,009

Kramariuk Patent, from: www.uspto.gov - patent no. 1,542,148

Turner Patent, from: www.uspto.gov - patent no. 2,836,421

Pidgeon Patent, from: www.uspto.gov - patent no. 4,148,489

Derouin Patent, from: www.uspto.gov - patent no. 4,880,238

Dykstra Patent, from: www.uspto.gov - patent no. 5,040,797

Rob's Puzzle Page, from: http://home.comcast.net/~stegmann/interlocking.htm

Cutler's Holey 6PB Booklet, from: http://home.comcast.net/~billcutler/docs/H6PB/index.html

Cutler's Computer Analysis, from: http://home.comcast.net/~billcutler/docs/CA6PB/index.html

IBM Burr Page, from: http://www.research.ibm.com/BurrPuzzles

Curfs' Page, from: http://home.tiscali.nl/~bcurfs/homepage/burrs/burrs-e.htm

Math Games Page, from: http://www.maa.org/editorial/mathgames/mathgames_08_02_04.html

Wikipedia Burr Page, from: http://en.wikipedia.org/wiki/Burr_puzzle

Mathematische Basteleien Page, from: http://www.mathematische-basteleien.de/devilsknot.htm

Mr. Puzzle Page, from: http://www.mrpuzzle.com.au/category129_1.htm

Source Forge Page, from: http://burrtools.sourceforge.net/gui-doc/BurrDesignTools.html

Interlocking Puzzles,

circa 2000.

(3 wood pieces, 2.75")

Daniel C. Alsmeyer 2006,

Sabriday Puzzles.

(3 wood pieces, 3")

"Triple Cross",

Puzzles & BT 2006.

(3 wood pieces, 3.2")

Three examples of the wood knot that was patented byM. P. Raoin 1980. Here are the directions that were sold with the Sabriday version:

Further reading:

Rao Patent, from: www.uspto.gov - patent no. 4,198,053

a.k.a.Three Piece Puzzle

Purchesed from Puzzles and Brain teasers Ebay Store 2006.

(three wood pieces, 3.75 inches;

described on pages 106 and 139 of the 1983Hoffmann book)

Designed and made by Interlocking Puzzles, circa 2000.

(walnut, paduk, and hard maple, 3 inches square)

Unlike the common three piece wood knot, there are no identical pieces:

Designed by Oskar Van Deventer, purchased from Bits And Pieces, 2008.

(metal, 1.4 inches)

Here are photographs of the three pieces being disassembled:

Here is the solution sheet that was sold with the puzzle:

Designed by Oskar van Deventer 1983.

Made by Tom Lensch.

Sold by Cubic Dissection 2005.

(three wood pieces and solution figures, 3 inches)

Designed by Ronald Kint-Bruynseels, made by Eric Fuller 2006, Level 8.

(wood, 3 inches)

Here are the 8 assembly steps:

Designed by Wilhelm Segerblom in the late 1800's.

(three wood pieces, 2.25 inches)

TheIBM Burr pagecites the April 1899 issue ofScientific Americanas publishing this puzzle. Three identical pieces each have outer dimensions 2 by 2 by 6 units. Each has all of the center 2 by 2 by 2 portion removed except for a 1 by 1 by 2 rod that is beveled at 45 degrees (a total of 7 units of wood has been removed from each piece). To assemble, all three pieces have to be slid together simultaneously (an outside surface of the rod slides perpendicular to one piece while the beveled surface slides over the corner of another). It is not possible to put two pieces together and then slide the third one in. The figure below shows the three identical pieces in the orientation to be put together.

Further reading:

IBM Burr Page, from: http://www.research.ibm.com/BurrPuzzles/

Designed by R. Stanton, made by E. Fuller 2008.

(Curly Maple, 3 inches)

Three identical piece slide together simultaneously to make a 3-dimensional cross.

Hold one piece vertically and determine how a second piece fits (there are only a few possibilities; look for the one where two faces sit nicely together), then carefully slide it out and put that piece down on the table without disturbing its orientation, then do the same for the third piece. Now that you have determined the orientation of the three pieces, hold them in their orientations so that they are just on the verge of engaging, line everything up, and then just squeeze the three together.Assembly:

Randomly jiggle and push on the pieces until you can get it to come apart just a bit. You can keep doing this until the puzzle comes apart, but as it comes apart a bit you should be able to find the right way to hold on to and push two of the pieces so that the puzzle slides apart, and you can just push and pull to make it expand and contract, where the third piece is being controlled by the movement of the other two that you are holding.Disassembly:

Here are two views of the puzzle in a partially expanded state:

Designed by Dic Sonneveld, made by Tom Lensch, circa 1990.

(Walnut, 2.25 inches)

Three identical pieces come apart in simultaneous motion:

Designed by Jim Gooch,

made by Eric Fuller,

purchased from www.cubicdissection.com.

(three wood pieces, 2.9 inches)

At first this appears to be a three piece burr made with excess play in the fit. However, the extra play is just enough so that these three identical pieces come apart with a non-rectilinear movement.

Designed by J. Krijnen, made by E. Fuller 2008, unique level 7.

(Quilted Sapelle, 3 inches)

Here are steps ito dissassemble:

Designed by O. Yamamoto, made E. Fuller 2008, unique level 4 with a twist.

(Walnut, 3 inches)

Here are steps ito dissassemble (there are two photos for the second step, which is a twist):

Designed by T. Jolly, made by E. Fuller and sold by Cubic Dissection 2008, level 6.

(Bloodwood, Wenge, Holly, 3 inches)

When assembled, one can look through the center holes in any of the three directions. Here are photographs of the six steps to disassemble, where step 2 is a twist:

Designed by Bill Cutler 1999, made by Jerry McFarland, level 8.

(left: GigaBurr -Walnut, 2.2 inches; right: GigaBurr II - Cherry, 2.2 inches)

The 250 billion puzzles of this type were enumerated with a computer by Bill Cutler. The highest level (moves to remove the first piece) was 8, of which there were 80 different puzzles, where only 3 had only 9 internal voids. Two of these are theGigaBurrandGigaBurr II, and the third is a symmetric version of the GigaBurr II. To solve, two pieces can go together only one way, and then visualize the third piece in its final position to determine how to get it in and out. Here are photos of solving (the third sequence shows the symmetric GigaBurr-2 made by someone else):

Designed and made by Bill Cutler and Jerry McFarland 2001, level 6.

(left: Poplar / Walnut, 2.2 inches;

right: Cherry / Walnut / Wenge, 2.2 inches)

The basic design of the 3-pieceGigaBurrandGigaBurr-2was expanded to a 5x5x5 cube by gluing on edge and corner pieces. Cutler's computer search yielded three basic level 6 puzzles, of which these are two.

Designed by Bill Cutler.

(Walnut, 3.5 inches)

Four irregular shaped pieces and two ball bearings, which when assembled, look like a 6-piece burr. Falls apart easily.

Designed by Jim Gooch, made by Eric Fuller, level 9.

(Pau Amerillo / Wenge / Bocote, 3 inches)

The pieces consist of a "block", two identical "rods" in symmetric orientations, and two identical "plates" in symmetric orientations. Orientate the puzzle as shown on the left below (the right rod will drop down as shown if the puzzle is not too tight), exchange the plates by passing them through each other, then the right plate (which was the left plate) can be twisted (in two ways) and removed (or without twisting it can be slid out together with the right rod).

Designed by William Hu, made by Eric Fuller, 2014.

(4 pieces, White Oak, Chakte Viga, 2" x 2" x 3")

This is what the puzzler maker says about the puzzle:"This seemingly simple puzzle uses a very interesting and difficult type of rotation. Ultra tricky and not like anything I've tried before. Level nine and fun...watch out, this one will have you pulling your hair out! Construction was tricky...the solid side spine and endgrain key pieces were fun to make, but very labor intensive. Fit is excellent; may be difficult to solve in highly humid environments due to the very close tolerances involved."At first it looks like there is no way for it to come apart. If we number the pieces 1, 2, 3, 4 going from left to right, the trick to dissassembly is to tilt piece three and rotate piece two 90 degrees (clockwise as you look through the puzzle from left to right). The puzzle generally has a nice loose fit, but it is a tight fit at the point of the rotation.

Designed byStewart Coffin, purchased from Cubic Dissection circa 2006.

(five wood pieces, 3.5 inches)

The 5 pieces give the appearence of four sets of two. The solution is not unique.

Old design, level 1, no holes, notchable.

(six wood pieces, 3 inches)

The basic idea of level 1 with a key piece is described on pages 106 and 139-140 of the 1983Hoffmann book. This one is even simpler. Pieces 1, 2, and 3 are identical, pieces 4 and 5 are identical, and piece 6 is a simple solid "key" piece that comes out first.

1. 2. 3. 4. 5. 6.

Assembly:1. Place pieces 1 and 2 together to form an empty rectangle shape.

2. Lay piece 3 in the bottom of the empty rectangle.

3. Place pieces 4 and 5 on either side.

4. Slide in piece 6.

Made in Indonesia 2004.

(wood, 3 inches)

Made in Indonesia 2004.

(wood, 3.2 inches)

Purchased in the 1970's.

(plastic, 2.5 inches)

a.k.a.Double Cross

Made in Japan, circa 1930?, level 1, no holes.

(six wood pieces, each 5/16 inches square by 2.4 inches long)

Another example of aSimple 6-piece Burr. Also in the theme of pages 106 and 139-140 of the 1983Hoffmann book, but also simpler. Two identical pieces form an empty rectangle, a double notched piece goes in the bottom, two identical pieces go on each side, and the key piece slides in:

Old design, level 1, no holes, notchable., circa 1960s-1980s??

(six aluminum pieces in a cardboard box, 2+3/8" x 2+3/8" x 1/2";

directions on the back of the box are shown above)

"Made by U.N. Co. N. Y.", circa 1920?, level 1, no holes, notchable, 2x2x8 pieces.

(cardboard box, 3.2 by 2.2 by 5/8 inches, and six 1/2" x 1/2" x 2" wood pieces)

Along wth theYamato Block Puzzle, this puzzle is discussed on page 262 of thePuzzlers' Tribute Bookin a chapter by Jerry Slocum and Rik van Grol on antique Japanese export puzzles. They show a picture from the 1915 C. J. Felsman Catalog of a Mikado puzzle saying "A problem of problems ...", and note that the sililar language here, "The puzzle of puzzles ...", is further evidence that although it says NY, it may in fact be a Japanese import. Here is what is on the cover and the inside of the cover:

"Made by U.N. Co. N. Y.", circa 1920?, level 1, no holes, notchable, 2x2x8 pieces.

(cardboard box, 3.2 by 2.2 by 5/8 inches, and six 1/2" x 1/2" x 2" wood pieces)

Along wth theMikado Block Puzzle, this puzzle is discussed on page 262 of thePuzzlers' Tribute Bookin a chapter by Jerry Slocum and Rik van Grol on antique Japanese export puzzles. Here is the solution sheet that came with it and a photo of another one of these puzzles where someone has labeled the pieces:

Made in Germany, level 1, circa 1940's?

(six wood rods, 3/8" square by 2+3/8" long, with solution sheet, in cardboard box)

"Pheno-Caffein Co.,Worchester, MA, circa 1910.

(wood, 2.1 inches)

The Pheno-Caffein Co. also made theSectional Checkerboard Puzzle, and like that puzzle, one could obtain a solution:

Designed by Stewart Coffin level 3, 3 holes.

(six wood pieces, 3.5 inches)

Designed and made by Bill Cutler 1984, unique level 5, 7 holes.

(Red Oak, 3 inches; 24 assemblies with a unique solution)

Discovered (by computer) and made by B. Cutler 1987, unique level 5, 7 holes.

(Mahogany, 3 inches)

Discovered (by computer) and made by B. Cutler 1988, unique level 7, 3 holes.

(Cherry, 3 inches)

Discovered (by computer) and made by B. Cutler 1988, unique level 8, 4 holes.

(Maple, 3 inches)

Designed by B. Cutler, made J. McFarland 2009, unique level 8, 7 holes.

(Maple / Walnut / Cherry, 2.8 inches)

Here are the first six steps:

Now the leftmost piece can be lifted up and out:

Discovered (by computer) and made by B. Cutler 1988, unique level 9, 5 holes.

(Walnut, 3.5 inches)

Designed by P. Marineau, made by J. McFarland 1986, unique level 9, 7 holes.

(Walnut, 3 inches)

Designed by Bill Cutler 1990, unique level 10, 7 holes.

(Mahogany, 3.5 inches)

One of 18 similar unique level 10 burrs discovered by Bill Cutler with a computer program. It can be disassembled by moving (1) C /E forward 1 unit, (2) F up 2 units, (3) A back one unit, (4) D /F right 1 unit, (5) F down 2 units, (6) F forward 1 init, (7) D left 1 unit, (8) A/E back one unit, (9) B/C/F right one unit, (10) B down one unit. Note that some would consider this 11 moves since for "move" 8, both A and E can move back without dragging the other. To assemble, rather than inserting B into the pieces appropriately oriented, it may be easier to orientate things with CD facing up, and hold A/D/E (appropriately positioned) in your left hand and B/C/F (appropriately positioned) in your right hand to perform steps 10 and 9.

Discovered (by computer) and made by B. Cutler 1987, level 10, 9 holes, notchable.

(Maple, 3.6 inches)

Non-unique with solutions below level 10, but made to be unique level 10 by drawing diagonal lines on the pieces that must form a loop around the puzzle when solved.

Designed by Brian Young, made by Mr. Puzzle Australia, level 10, 8 holes.

(4.7 inches)

Unique Level 10 solution. One more hole thanComputer's Choice Unique-10, with 20 assemblies instead of 7. Here is the solution that was sold with it:

Designed by Bruce Love 1987, made by Bill Cutler, level 12, 9 holes.

(Maple, 3 inches)

According toBruno Curfs' page, Love's dozen has 89 solutions ranging from Level 3 to one of the solutions being level 12; this puzzle made by Bill Cutler has a big D drawn on a pair of the ends that forces the level 12 solution.

Further Reading

Curfs' Page, from: http://home.tiscali.nl/~bcurfs/homepage/burrs/burrs-e.htm

Designed and made by Bill Cutler; can't be disassembled.

(Red Oak, 4.5 inches)

From his computer analysis, Cutler determined that 139 was the largest number of states that a standard 6 piece burr could have without having a solution, and then he chose the simplist of these for this puzzle. So this burr is made to the dimensions of a normal 6-piece burr, has lots of movement, but can't be disassembled (it was made by gluing two portions of a piece together during assembly).

Purchased from Mr. Puzzle Australia 2006, level 1, no holes.

(six wood pieces, 3.5 inches)

Mr. Puzzle Australia credits this puzzle as being sold as early as 1875, and as having been sold under a number of names, including theCluster, theGem Cut Puzzle, theChestnut Burr, and theSnowflake. When assembled it looks like a standard version of theSimple Six Piece Burr(where pieces have a diamond cross section). However, it actually is composed of six identical pieces where two assemblies of three slide together.

Made in Japan circa 1930?, level 1.

(cardboard box and 6 wood pieces, 3.75 inches;

box cover similar to other vintage Japanese exports like theYamato Puzzle)

Made in Japan circa 1930?, level 1.

(cardboard box and 6 wood pieces, 3 inches;

box cover similar to other vintage Japanese exports like theYamato Puzzle)

Here is the solution sheet that came with it:

Designed by Bill Cutler 1965, purchased circa 2000, level 1.

(six wood pieces, 3.5 inches)

Six identical pieces with some angled internal cuts that slide apart simultaneously.

Discovered (with a computer) and made by Bill Cutler 1989, level 5, 7 holes.

(Maple, 3.5 inches)

A programmer's nightmare because disassembly requires a twist. Move F up 1/2 unit, rotate A 90 degrees, move A up (pulling F with it by 1/2 unit), move D up, slide D out. Note that although the 1/2 move is needed theoretically, there is enough play in the puzzle that F can initially be moved up a full unit (this does not change the level since A has to be moved up in any case). This puzzle is hard for a person too, because according to Cutler's computer analysis, there are 102 assemblies (ways these pieces can exist in space in the solved shape) with only this one solution (the only way that is achievable starting with the pieces apart).

Designed and Made by Bill Cutler 1994, level 7, 4 holes, notchable.

(Cherry, 2.25 inches)

Bill Cutler credits Stewart Coffin with the idea of making burrs with slanted pieces in a way that restricts the number of possible assemblies. Cutler then found a non-unique level 7 burr from his computer analysis which became unique when made with slanted pieces. Slide F forward, slide E left (pulling D with it), slide E forward, push D right, slide F back, slide F right, remove A:

Designed by Bill Cutler.

(Walnut, 3 inches)

Slide F back and then remove the three pieces A, C , E simultaneously by expanding them out to the upper left:

Designed by Bill Cutler1986, spin + level 3.

(Red Oak with two steel ball bearings, 3.5 inches)

Spin the puzzle in the orientation shown (around the axis defined by E and F) to position the balls, and then the two halves A,C,F and B,D,E can slide apart with three moves:

Designed by Gregory Benedetti, made by Maurice Vicourouz 2012.

(Purple Heart, 3.25 inches)

Pieces are a small cube trapped in the center, three identical "simple pieces", and three identical "complex" pieces. Assembly is relatively easy, where the three complex pieces and the cube are put compactly together as shown on the left in the figure below (rubber bands keep them together for the photo) and then the three simple pieces slide simultaneously over the exposed corner:

Disassembly requires simultaneous motion to move the three complex pieces together into the "key position" shown on the left below. One first has to identify which three are the complex pieces and then carefully jiggle and push to get all three to push in flush. In the middle is this position lit up from the back (where the serial number of the lower in-out piece can be seen), and on the right is shown the top three pieces coming apart simultaneously. The puzzle's name comes from the fact that when you don't know what is inside this puzzle, disassembly may be achieved by accident when randomly shaking and pulling on the puzzle.

Designed by Matti Linola, made by Eric Fuller 2010.

(Yellowheart and Wenge, 3 inches)

Once one sees how to solve the three piece burr formed by the light colored pieces, the dark pieces don't change the puzzle very much, but the construction and fit is terrific.

To solve:Here are photos of the assembly progressing:

- Take out the dark pieces, to first solve the 3-piece burr.
- Start with the simple U shaped piece and see that because each piece has to slide over one of the other two, there is only one way the other two can go, and then assemble the three pieces.
- Now look down each end, and it can be seen that there is only one way the dark pieces could possibly fit.
- Then take apart the three light pieces, insert the dark pieces, and push everything back together, moving the dark pieces in and out as needed.

Designed by Frans de Vreugd 2005, purchased from Mr. Puzzle Australia.

level 5, 3 hole, notchable, six 2x2x6 pieces with end caps.

(Queensland Silver Ash with Queensland Blackbean ends, 3.125")

A variation of the standard 6 piece burr where end caps have been added to the pieces; highest level for this type of burr with notchable pieces. Here is a diagram of the puzzle and the pieces (numbers are the order they can be removed):

Designed by Stewart Coffin (puzzle no. 9), made and sold by Interlocking Puzzles 2000.

(wood, 6 identical pieces and 6 corresponding identical pieces, 2.6 inches)

A variation of the 1890Altekruseburr with pins and holes for some of the notches; shown on page 79 of theCoffin Book. Below are photos of one way for inserting pieces 3 through 11; piece 12 is then added to complete the two halves as shown above, which then slide together.

Designed by Frans de Vreugd, purchased from Bits and Pieces 2007, level 6.

(wood, 3.75 inches)

Designed by Stewart Coffin (design number 105)

Sold in 2006 by Cubic Dissection (www.cubicdissection.com)

(left Bocote / right Cocobola, both 3.25 inches)

Can be solved in two ways using the same pieces; the left above is solved using coordinate motion (all pieces moving together at the same time), and the right above is solved by halving two halves that slide together. The hardest part is trying to visualize what it should look like together once it is apart. Here is what the two solutions look like when starting to come apart:

Designed by Stewart Coffin, Made by Eric Fuller 2012.

(Canarywood, a 13/16" cube and 6 pieces 3" long by 13/16" square)

The six pieces assemble with coordinated motion into a standard 6-piece burr shape with the cube trapped in the middle. I found the maniputlation of these pieces a bit unpleasant and gave up (at least for the moment - it would have probably felt better if I had solved it). Here is the description quoted from the puzzle maker's page:"This puzzle was Jarry Slocum's exchange puzzle at IPP18. I was recently visiting a puzzle friend and saw it on the shelves. Spent some time working with it and finally solved it... HAD to make it. Since John Rausch did such a nice job writing up a description on his site, I think I'll plagarize from it directly:"Four of the six pieces have diagonal notches on both sides of the large, simple notch. Two pieces have them on only one side. Normally, a six-piece burr consisting only of pieces with a single, large, simple notch could not be assembled. With the diagonal notches described, it becomes a coordinate motion puzzle - a difficult one! Number 129a in Stewart's numbering system. He made 100 in 1998."I have modified the design a little bit based on Nick Baxters advice - instead of two pieces having only one notch, one piece does (leaving the other five with double notches). After some experimentation I felt that this configuration was the trickiest, and really made the solver grasp the concept behind the puzzle. Finaly, this puzzle is by nature very loose when solved. It's just a function of the notch location. I hate loose puzzles, so I included a 7th piece, which is an internal cube with magnets. This doesn't really add to the assembly, but it keeps the puzzle nicely together once solved. Happily it also makes the puzzle much more difficult to disassemble!"

a.k.a.Triple Play

Purchased from Bits and Pieces 2007.

(wood, 3 inches)

Looks like three pieces but is actually a level 1 non-standard 6 piece burr (six pieces (three light wood and three dark wood pieces). Here is the solution that came with the puzzle:

Designed by F. Potts, made by E. Fuller 2008, purchased from Cubic Dissection.

(Walnut and Maple, 3 inches)

Six pieces with magnetic tips assemble to look like a three piece burr (e.g.,Just The Three). The pieces are all identical; here are photos of different views of them:

Here are photos of pulling apart the whole assembly and an assembly of four:

The solution is almost as much of a dexterity puzzle as a logic puzzle, where there is only one way to put two together that will lead to a solution, then it is easy to spread them apart and put in the next two, then harder to spread apart the four to get in the fifth, and then after pushing everything back together, a bit tricky with only two hands to get in the sixth piece. Here is a photo of the assembly of four with the two remaining pieces still to be put in:

Designed by Gregory Benedetti, made by Eric Fuller 2011.

(Acrylic, Yellowheart, 2.25 inches)

Here is what the puzzle maker said about this puzzle in the sale listing:"Reminiscent of Padaung Rings, this nifty little pocket puzzle is a lot of fun to solve. With a level 14.4.2 it's tricky but not impossible ... once you get the correct alignment and piece selection, it flows fairly quickly."

Copyright ThinkFun 2010.

(plastic, 2.75 inches square)

Comes with a solution booklet that has 37 steps to disassemble reading forward and 37 steps to assemble by flipping over the booklet and reading in the other direction.

Further Reading

Booklet pages.

Designed by Chi-Ren Chen, made by Eric Fuller 2012, unique level 2.

(Walnut, Ash, American Mahogany, 3")

Designed (with a computer) by Bill Cutler and Frans de Vreugd 2001, level 13

(Hard Maple and Jatoba, 2.25 inches)

Two 1x4x6 pieces in each dimension. Making top dark wood and the bottom light wood makes the level 13 solution unique. The number of "holes" (internal voids) is 13 because the volume of assembled shape if it was solid is 104, and adding up the volume of the six pieces gives 91. Here are sheets that came with the puzzle (copyright by and courtesy ofBill Cutler).

Purchased from ThinkFun 2006.

(plastic, 6 pieces, 2.75 inches)

Made by D. Alsmeyer 2007, Sabriday Puzzles.

(6 different woods, 3.5 inches)

The booklet that comes with the retail plastic puzzle shows 65 steps to completely take the puzzle apart.McFarren's Pageshows a solution that removes the first piece in 28 steps, and completely takes the puzzle apart in 35 steps.

Further reading:

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/gordian.htm

Sabriday's wood description(Mahogany, Maple, Cherry, Purpleheart, Walnut, Paduk).

Designed and made by Franz de Vreud 2003, unique level 16.

(Maple and Granadillo, 2.9 inches assembled)

These were made in Japan and owned by J. A. Storer in the 1960's. TheCleverwood Pagecredits these simple types of burrs toTsunetaro Yamanaka(born 1874) and his descendants; here is a diagram of a cube from the 1942Filipiak book, and an inexpensive circa 2000 plastic ball:

Further Reading

Cleverwood Page, from: http://www.cleverwood.com/kumiki.htm

Wm. F. Drueke & Sons, Grand Rapids, MI, circa 1940's?

(wood pieces in cardboard box, 2+5/8" x 2+5/8" x 2+5/16" high)

Examples of some classic relatively simple burrs that have been made by many over the years (e.g., see theJapanese Shape Burrs). Historical acounts indicate that Bill and Marian were Drueke family names.

Further Reading

Drueke Family History, from: www.peterspioneers.com/WRSD.htm

Drueke Directory, from: www.peterspioneers.com/WRSDdir.htm

C. Bloom Grand Rapids Press Article, from: www.peterspioneers.com/WFD.htm

Cribbage Board Article, from: http://www.cribbageboardsonline.com/article2005b.pdf

Designed by Junichi Yananose, made by Eric Fuller.

(7 wood pieces, 3 inches)

Looks at first like a standard 6-piece burr. However, one of the apparent pieces is really two pieces.

Made in Japan, circa 1930?, level 1, no holes.

(cardboard box, 2.6" x 2.1" x 7/16", 9 wood pieces, and solution sheet;

box cover similar to other vintage Japanese exports like theYamato Puzzle;

this puzzle was also made in a22-piece version)

Here are photos of basic solution steps:

"Patent number 35588, Made In Japan", circa 1920's?

(10 wood pieces in a 3.75" x 2.4" x 1/2" cardboard box)

Easy to see how it goes together, but a bit of a dexerity puzzle to put the final piece in; two of the rectangle pieces have bevels to make that work (on on the inside middle and one on both edges).

Designed by P. McDermott, made by B. Young and P. McDermott,

purchased from Mr. Puzzle Australia in 2007, level 6.

(wood, 10 pieces, 3.25 by 6.25 by 2.5 inches)

Here are the directions and solution that were sold wih the puzzle:

Designed by Bill Cutler.

(wood, 3.5 inches, 11 pieces and 5 ball bearings)

Eleven pieces in a 2-4-5 configuration. Takes 5 balls (it came with 4 inside and you are asked to put the 5th in). Two are in a notch near the top of 11. The other three can be in a portion of the bottom part of piece 11 when it is pushed up, but in order to get 11 in place, they must be shaken out into other places that lock up the other pieces. Number the ends as follows:

Disassembly:1. Jiggle the balls if necessary and move 11 up. 2. Two balls are always in a notch near the top of 11; jiggle the other three so that they are in a cavity at the bottom of 11. 3. Slide 8 up (1 and 2 get dragged with it). 4. The balls will now all fall out. 5. Slide 5 out. 6. Slide 11 out. 7. Slide 3 and 10 out. 8. Remove 7 and 9. 9. Remove 4. 10. Remove 6. 11. 1, 2, and 8 now come apart.Assembly:1. Assemble the puzzle without the balls by reversing the disassembly. 2. Slide 11 and 8 up (8 gets 1 and 2 dragged with it). 3. Put the two balls in the top and then slide a pencil through the puzzle to keep them from coming out. Then turn the puzzle over and put the other three balls in. 4. Slide 8 down (dragging 1 and 2 with it) as you carefully remove your pencil. 5. Shake the three balls so they leave the bottom of 11; then slide 11 down.

a.k.a.Hexsticks, Notched Hexagonal Sticks

Patented by S. Coffin 1973, made by 3M 1970,

also discovered independently by B. Cutler.

(12 plastic pieces, 3.5 inches)

Three solutions for assembling the twelve notched sticks are described on pages 116-118 ofCoffin's book. The package is shown above; it has the directions on the bottom (also shown above) and inside is a hexagonal shaped solution booklet. Below are two panels from each side (other three are shown on the next page):

Further Reading

Coffin Patent, from: www.uspto.gov - patent no. 3,721,448

Cutler's Hectix Page, from: http://home.comcast.net/~billcutler/stock/hectix.html

Cutler's Hectix Revisited Page, from: http://home.comcast.net/~billcutler/stock/revisited.html

S.S. Adams Co., 1961.

(12 plastic pieces, each 1.5 by 3/8 by 3/8 inches)

S.S. Adams Co., 1961.

(12 plastic pieces, each 1.5 by 3/8 by 3/8 inches)

Purchased from Bits and Pieces 2007.

(10 wood pieces with solution sheet, 4.5 inches;

shown as "The Mystery" on pages 107-108, 141-142 of the 1893Hoffmann book)

Copyright 1991-2007 Junichi Yananose, purchased in Japan 2010.

(aluminum, 12 pieces, 3.5 inches square)

Here is the box and the text on the front and back:

The puzzle slides apart in two halves and a free piece:

Designed by Bill Cutler and made by Jerry McFarland 2003.

(Walnut, 12 pieces, 2 by 2 by 8 inches)

Here is the sheet that came with the puzzle (copyright by and courtesy ofBill Cutler):

Designed by Bill Cutler 1981.

(Maple / Walnut / Cherry, 3.7 inches, 12 pieces)

Designed by Bill Cutler 1982.

(Maple / Walnut / Cherry, 4 inches, 13 pieces)

Designed by B. Cutler in 1983, made by Mr. Puzzle Australia 2008, level 11.

(Queensland Silver Ash / Queensland Blackbean / Mackay Cedar, 14 pieces, 4";

sold with directions and solution shown above)

Designed by B. Cutler 1984, made by E. Fuller 2008.

(Maple / Walnut / Mahogany, 15 pieces, 4 inches)

Designed by Bill Cutler and made by Jerry McFarland 2000.

(wood, 3 inches, 13 pieces + 2 pins)

Looks like the Wausau '82 puzzle, but different inside; here are excerpts from the puzzle sheet (copyright by and courtesy ofBill Cutler):

- Position the puzzle on a table so the group of three are vertical and the group of six with the dot is facing you, with the dot on the right (upsidedown from the figure).

- Give the puzzle a hard spin clockwise to move the pins into their holes.

- Simultaneously, the center rod of the three goes up, the rod with the dot comes out toward you, and the rod to its left goes back away from you. You will see the pins in the ends of the rod with the dot and the one next to it (take them out so you don't lose them).

- Now the puzzle comes apart.

Designer unknown, made by Eric Fuller.

(Purpleheart / Maple / Lacewood, 13 pieces, 2.25 by 3 by 3.75 inches)

Here is what Eric Fuller says:"This 13 piece interlocking burr puzzle was published in the magazineSoumen Kuvalehtinumber 11 in 1926. There are 2 possible solutions, both very similar. Despite its not being a high level puzzle, the solution is surprisingly tricky, probably because of its unusual shape. Ishino Keiichiro posted it on his site and Matti Linkola discovered the magazine."

Level 1, circa early 1900's??

(4" wood box with directions and 18 wood pieces, 3.6 inches assembled;

right vertical piece in photo above is solid key piece.)

Designed by Bill Cutler 1975.

(Maple / Walnut / Cherry, 3.6 inches, 18 pieces)

Designed 1992 and made by Jerry McFarland, purchased from cubicdissection.com 2008.

(Walnut, Mahogany, Maple, 19 pieces, 3.5" by 2.6" high, 7/8 inch square sticks)

Disassembly involves manipulating the central 4 pieces like opening a lock.

Here is the diagram of the pieces from the solution sold with the puzzle and photos of removing three pieces:

Further Reading

Solution that was sold with the puzzle.

"Made in Japan K.K.", circa 1920's?

(20 wood pieces, 4 inches;

box cover similar to other vintage Japanese exports like theYamato Puzzle)

Two pairs of identical 4" pieces, four identical 2.5" pieces, eight identical 1.3" pieces, and four identical 1.3 inch solid pieces assemble to a somewhat two-dimensional snowfake arrangement; here is a photo of the box and the solution sheet:

Purchased from Pentangle Puzzles 2007.

(wood, 7.5 inches, 20 pieces)

Made in Japan, circa 1930?, level 1, no holes.

(cardboard box, 4.1" x 3.4" x 1/2", 21 wood pieces, and solution sheet;

this puzzle was also made in a9-Piece Version)

Designed by Bill Cutler and made by Jerry McFarland 2003, level 85.

(Cherry / Walnut, 21 Pieces, 3 by 3 by 3.6 inches)

The Binary Burr functions like theChinese Ringspuzzle:

There are six "ring" pieces that must be manipulated in order to remove the "bar" piece; the remaining 14 pieces don't move and form the "cage' that constrains the movements. It basically takes two moves for each move of the corresponding Chinese Rings puzzle.

Designed by Bill Cutler 1978, made by J. McFarland 2012.

(24 Maple, Walnut, and Cherry3/4" rods, 5.25" square assembled)

Designed by Bill Cutler 1978, made by J. McFarland 2012.

(24 Maple, Walnut, and Cherry3/4" rods, 4+3/8" square assembled)

PDesigned by L. Kleinwaks, made by Eric Fuller 2013.

(Walnut, Cherry, Maple, 2.25" x 2.25" x 4")

Purchased from Interlocking Puzzles 2000.

(wood, 2.5 by 2.5 by 9.8 inches)

Four standard 6-piece burrs that share one dimension. Pieces 4, 8, and 10 are identical, pieces 1, 5, and 15 are identical, pieces 12 and 16 are identical, pieces 11 and 14 are identical, and pieces 9 and 13 are identical:

Designed by Wayne Daniel 1982, made by Interlocking Puzzles.

(wood, 4.8 inches)

a.k.a.Eight Burrs

Designed by David Bruce, made by Interlocking Puzzles 2000.

(wood, 24 pieces, 4.8 inches)

The basic idea is to combine two eight piece assemblies and then add eight "outer" pieces. Here are diagrams of the pieces from the solution that came with the puzzle:

Assembly A pieces:

Assembly B pieces:

Outer pieces pieces:

Further Reading

Lost Day solution that was sold with the puzzle (pdf 9 pages).

Purchased from Interlocking puzzles 2002.

(13 ply Baltic Birch rings 7.2", Australian Jarrah rods 2.25", 18 pieces)

Four 6-piece burrs connected in one dimension by a pair of rings. Requires multiple counter rotations of the rings to disassemble or assemble. Interlocking Puzzles said:

"The eight radial pieces have slightly angled notches and can be sorted into four right handed and four left handed pieces. The eight axial pieces have normal notches. The four unique higher level burrs are distinctly different. The lengths of the burr rods are greater than 6 units. If these were four stand alone burrs they would require five, four, or three moves to get the first piece out. One of them would also require three moves to get the second piece out. It is a fun challenge to assemble each individual burr onto the rings and then remove it before facing the larger challenge of the whole puzzle."

Purchased circa 2000.

(plastic, 2.25 inch cube with 3D cross)

Similar idea to theTwo Piece Oddity, with a frame and a 3D cross like piece that has to be removed.

Designed by Tom Jolly, made by Eric Fuller circa 2000.

(T'Zalam, 3 inches)

A frame and a 3D cross like piece that has to be removed.

Designed by Osanori Yamamoto, made by E. Fuller 2013, Level 14.

(Jatoba and Purpleheart, 2.25" x 1.5" x 1.8")

To disassemble, exchange the two trapped pieces, maneuver a bit, and then the two can be manipulated out of the cage; here are some selected positions:

Designed by Stephane Chromine, made by Eric Fuller, 2011.

(Walnut and Yellowheart, 3" x 2.25" x 1.5")

The top two pieces are identical. Different assemblies are possible depending on how the top two pieces are rotated. In their easiest positions, the bottom piece can be removed in 8 moves. However, in one configuration, 12 moves are required to remove the bottom piece (given a reasonable way of counting rotations). Below are 9 of the positions for disassembly starting with the top piece rotated as the puzzle was shipped. Although the middle piece starts in its correct rotation for the final steps of disassembly, after pulling out and tilting down the bottom piece, the middle piece is rotated and drops down to allow the top piece to be rotated, and then the middle piece can be pushed up and rotated back so that the top two pieces are together and up to allow the bottom piece to be removed. Note that it now takes only 8 steps to put the puzzle back together by leaving the top two pieces in their existing rotations.

Designed by Ramos & Abad, made by Pelikan 2006, level 13.

(wood, 2.4 inches)

a.k.a.Internal Combustion

Designed by Tado Muroi early 1990's.

(left: "Pandora's Box", Mr. Puzzle Australia, Queensland Blackbean, 3.5x3.5x2.25";

right: "Internal Combustion", Bits and Pieces, Aluminum, 2.25" x 2.25" x 1.5";

described inBoardman's book)

Four burr pieces (two of which are identical) in a frame. Below is a 9-step assembly (6 steps to remove the first piece) based on the piece orientations shown on the right above (except in the photo above the left two have been flipped upside-down for better viewing):

1. 2. 2.

4. 5. 6.

7. 8. 9.

A 12-step assembly where the piece labeled 3 is reversed from the 9-step assembly shown on the preceding page:

A 15-step assembly (see also the Boardman book):

Designed by Yavuz Demirhan, made by Eric Fuller 2013.

(Sapele and Imbuya, 2.25" square, level 4)

Purchased from Bits And Pieces, 2008.

(wood, 3.4 inches square assembled by 7/8 inches thick, with solution sheet)

Designed by Gregory Benedetti, made by Eric Fuller 2012.

(Sapele and Wenge, two halves of the cage and 6 pieces, 2+5/8" square)

Designed by Logan Kleinwaks, made by Eric Fuller 2013.

(right, "Bookend Burr", Holly, Walnut, Ash, 2.5"x2.25"x2.75", level 10;

(middle, "Clamped Burr", Holly, Walnut, Ash, 2.25"x 3"x2.6", level 15;

right, "Cornered Burr", Walnut, Cherry, Ash, 2+5/8" square, level 14)

Beautifully made with high levels for rectlinear moves solutions. Shorter solutions may be possible with non-rectilear moves. For example, to remove a piece from the Cornered Burr with just three moves and some additional twisting, start by sliding the top piece to the right (if it looks like on the left below, re-orient the puzzle so it looks like the right photo below), then slide the front piece left, then up, and now, although it is easier by first sliding the bottom piece to the right, it can be twisted out without any further movement of other pieces.

Sold by Interlocking puzzles 2000.

(wood, 2.5 inches)

The only set of 6 notchable pieces that can be assembled into 6 different level 1, no-hole, standard six piece burrs. Here is the solution that was sold with the puzzle:

Designed and made by Jean-Claude Constantin, purchased used 2006.

(13 pieces, set is 6.25" x 3.25 x 2.5 inches, each piece is 3/4 x 3/4 x 3 inches)

A set of 13 pieces to make 40 different notchable 6 pice burrs; the same set of 6 is sometimes used for several different problems (pieces in different positions). Each piece is 2 by 2 by 8 units.

JCC's 40 Problems:

1. ADFIKL

2. ADFIKL

3. ABDKLM

4. ABDKLM

5. ABDKLM

6. ACDKLM

7. ACDKLM

8. ACDKLM09. ADGHKL

10. ADEJKL

11. AFGIKL

12. AFIJKL

13. AEGIKM

14. AFHJLM

15. ADHIKM

16. ADEFLM17. ACGKLM

18. ACGKLM

19. ACJKLM

20. ACJKLM

21. ABGKLM

22. ABGKLM

23. ABJKLM

24. ABJKLM25. ADEIKM

26. ADEIKM

27. ADFHLM

28. ADFHLM

29. AGHIKM

30. AGHIKM

31. AEFJLM

32. AEFJLM33. BCFIKL

34. BCFIKL

35. BEFHIM

36. BEFHIM

37. BEFHIM

38. BEFHIM

39. BEFHIM

40. BEFHIM

JCC's Solution Hints:

1. AK-LI-FD

2. AL-KF-DI

3. AM-IK-BD

4. AL-MK-BD

5. AK-ML-DB

6. AD-MC-KL

7. AD-KC-ML

8. AD-LC-KM09. AL-KH-GD

10. AK-LE-DJ

11. AK-GF-LI

12. AL-JI-FK

13. AK-GE-MI

14. AL-JH-FM

15. AD-IH-KM

16. AD-FE-ML17. AL-KC-GM

18. AM-KC-GL

19. AK-LC-MJ

20. AM-LC-KJ

21. AK-MG-BL

22. AK-LG-BM

23. AL-MJ-KB

24. AL-KJ-MB25. AK-ME-DI

26. AM-KE-DI

27. AL-MH-FD

28. AM-LH-FD

29. AM-IH-KG

30. AK-IH-MG

31. AM-FE-JM

32. AL-FE-JL33. BI-LC-FK

34. FB-CK-LI

35. BE-HF-MI

36. BH-EI-FM

37. FH-EM-BI

38. EI-MH-FB

39. EH-FM-BI

40. EH-MI-FB

Purchased from Creative Craft House 2007.

(wood box 3.4" x 9.25" x 4.1" with 27 wood pieces, each 3.1" long by 3/4" square)

This set has 27 2x2x6 unit standard 6-piece burr pieces numbered from 0 to 26, where piece 0 is the solid piece. A total of 69 different level 1 standard 6-piece burrs can be selected, where all use piece 0 as a key piece, and the other 5 pieces are specified with a tic-tac-toe notation:

Made by Interlocking Puzzles 2000.

(7 x 6 x 3.4 inch Jarrah box with 42 Chechen pieces, each 3/4 x 3/4 x 2.4 inches)

25 distinct notchable 2 x 2 x 6.5 unit pieces, indexed from A to Y, a total of 42 pieces including duplicates, which can be used to assemble the 314 different level 1 six piece burrs that have no holes. The set comes with five puzzle cards and five solution clue cards that list the pieces in order from 1 to 6 according to where they belong in the diagram above. This set does not contain all possible notchable pieces; just has the pieces necessary (and enough copies) to make all 6-piece notchable burrs with no holes. Also, some higher level burrs can be constructed with this set; for example,L5 Notchableis OODXNL andHoley Astigmatismis TYLLUM. Note that because the pieces are more than 6 units long, there are some higher level burrs that don't quite work, but would if the pieces were exactly 6 units long.

1. Puzzle Descriptions 001 ALLXXX 022 CDPPYY 043 ADDVYY 002 BBTYYY 023 CDPPYY 044 ACMXYY 003 AHTYYY 024 CDPPYY 045 ADMXYY 004 AKTYYY 025 ALPXYY 046 AILOUY 005 ALLUXY 026 ALSVYY 047 AILOUY 006 BBXXYY 027 ALSWYY 048 AJLNUY 007 BETYYY 028 BCPXYY 049 AJLNUY 008 AKXXYY 029 BCPXYY 050 AKVXYY 009 ALSXYY 030 BDPXYY 051 AKWXYY 010 ACLUYY 031 BDPXYY 052 AMMXYY 011 ACLXXY 032 ELPTYY 053 BCPWYY 012 ADLUYY 033 AFLRYY 054 BCPWYY 013 ADLXXY 034 AGLQYY 055 BCPWYY 014 ALTUYY 035 ALMXXY 056 BDPVYY 015 LLPPXX 036 ALTVVY 057 BDPVYY 016 ACCXYY 037 ALTWWY 058 BDPVYY 017 ADDXYY 038 BBVXYY 059 CLPPXY 018 ALMTYY 039 BBWXYY 060 CLPPXY 019 AMSYYY 040 BLPXXY 061 DLPPXY 020 BLPTYY 041 LPPSYY 062 DLPPXY 021 BPSYYY 042 ACCWYY 063 ACLWXY 1. Puzzle Solution Clues 001 XXAXLL 022 PYPDCY 043 VYAYDD 002 YYBBTY 023 YPPCDY 044 XYAMYC 003 YYAHYT 024 YYPPCD 045 XYAMDY 004 YYAKYT 025 PXALYY 046 UYALOI 005 UXAYLL 026 YVAYSL 047 UYAOLI 006 XXBBYY 027 WYAYSL 048 UYALJN 007 YYBEYT 028 XPBCYY 049 UYANJL 008 XXAKYY 029 XYBPYC 050 XYAKYV 009 YYAXLS 030 PXBDYY 051 XYAKWY 010 UYAYLC 031 YXBPYD 052 MMAXYY 011 XYAXLC 032 YYPELT 053 YPBCWY 012 UYAYDL 033 RYALFY 054 YPBCYW 013 XYAXDL 034 QYALYG 055 YYBPWC 014 YYAULT 035 XXAMLY 056 PYBDVY 015 XXPPLL 036 VYAVLT 057 PYBDYV 016 YYAXCC 037 WYAWTL 058 YYBPVD 017 YYAXDD 038 XYBBYV 059 XPPCLY 018 YYAMLT 039 YXBBWY 060 XYPPCL 019 YYAMYS 040 XXBPYL 061 PXPDLY 020 YYBPTL 041 YYPPLS 062 YXPPLD 021 YYBPYS 042 WYAYCC 063 WXAYCL

2. Puzzle Descriptions 064 ADLVXY 085 AGLOVY 106 ANPQYY 065 AJRTYY 086 AFLNWY 107 ANPQYY 066 AIQTYY 087 AFLNWY 108 AOPRYY 067 AMPYYY 088 ANOSXY 109 AOPRYY 068 ANQSYY 089 ANOSXY 110 AOPRYY 069 ANQSYY 090 ANOSXY 111 BHNOTY 070 ANQSYY 091 BBVWYY 112 BLPVXY 071 AORSYY 092 BNQTTY 113 BLPWXY 072 AORSYY 093 BORTTY 114 LNPQTT 073 AORSYY 094 ANOTUY 115 LOPRTT 074 BCFRYY 095 ANOTUY 116 ACNOUY 075 BDGQYY 096 ANOTUY 117 ACNOUY 076 BFRTYY 097 BQRSYY 118 ACORXY 077 BGQTYY 098 BQRSYY 119 ACORXY 078 BMMUYY 099 ACNOXX 120 ADNOUY 079 ALNOUX 100 ADNOXX 121 ADNOUY 080 ALNOUX 101 ALMVXY 122 ADNQXY 081 ALNOUX 102 ALMWXY 123 ADNQXY 082 ALPVYY 103 ALQRXY 124 AINOOU 083 ALPWYY 104 ALQRXY 125 AJNNOU 084 AGLOVY 105 ANPQYY 126 AMNOTY 2. Puzzle Solution Clues 064 VXAYLD 085 VYAOLG 106 PYANYQ 065 RYAJTY 086 WYALFN 107 PYAYNQ 066 QYAIYT 087 WYANFL 108 OPAYYR 067 MPAYYY 088 NOAXSY 109 PYAORY 068 NQAYSY 089 NYAXSO 110 PYAYRO 069 QYANYS 090 OYAXNS 111 ONBHYT 070 QYAYNS 091 YYBBWV 112 XYBPVL 071 ORAYYS 092 QNBTYT 113 YXBPWL 072 RYAOSY 093 ORBTYT 114 QNPTLT 073 RYAYSO 094 NOAUTY 115 ORPTLT 074 YRBCYF 095 NYAUTO 116 NUAYCO 075 QYBDYG 096 OYAUNT 117 UYANOC 076 YRBFYT 097 QYBRYS 118 RXAOCY 077 QYBGYT 098 YRBQYS 119 RXAYCO 078 MMBUYY 099 NXAXCO 120 OUAYND 079 UXALON 100 OXAXND 121 UYAODN 080 UXANOL 101 XYAMLV 122 QXAYND 081 UXAOLN 102 XYAMWL 123 QXANYD 082 PYALYV 103 RXALQY 124 NUAOIO 083 PYALWY 104 QXALYR 125 OUANNJ 084 VYALOG 105 NPAYQY 126 NOAMTY

3. Puzzle Descriptions 127 AMNOTY 148 BDQRXY 169 BPQRYY 128 AMNOTY 149 CDPQRY 170 BPQRYY 129 BNOPTY 150 CDPQRY 171 BNOSUY 130 BNOPTY 151 CDPQRY 172 LNOPST 131 BNOPTY 152 CDPQRY 173 NOPPSY 132 BNOSTY 153 ENOPTY 174 NOPPSY 133 CFLPRY 154 ENOPTY 175 NOPPSY 134 CLPPWY 155 ENOPTY 176 AFNNOW 135 DGLPQY 156 HLNOPT 177 AGNOOV 136 DLPPVY 157 ACMVYY 178 AMNOXX 137 FLPRTY 158 ADMWYY 179 ANNQQX 138 GLPQTY 159 ALORVX 180 AOORRX 139 LMMPUY 160 ALORVX 181 ANOTVV 140 AIOTVY 161 ALNQWX 182 ANOTWW 141 AJNTWY 162 ALNQWX 183 ANOSVY 142 ANOPXY 163 AMQRYY 184 ANOSVY 143 ANOPXY 164 AMQRYY 185 ANOSWY 144 ANOPXY 165 BMPVYY 186 ANOSWY 145 BCQRXY 166 BMPWYY 187 COPPRY 146 BCQRXY 167 BFIORY 188 COPPRY 147 BDQRXY 168 BGJNQY 189 COPPRY 3. Puzzle Solution Clues 127 NYAMTO 148 QXBRYD 169 YPBQYR 128 OYAMNT 149 QYPDCR 170 PYBRYQ 129 NYBPTO 150 QYPRCD 171 ONBUYS 130 YOBPTN 151 YRPCDQ 172 ONPSLT 131 NOBPTY 152 YRPQDC 173 NOPPSY 132 ONBSYT 153 NOEPTY 174 NYPPSO 133 YRPCLF 154 NYEPTO 175 YOPPSN 134 YPPCLW 155 YOEPTN 176 OWANNF 135 QYPDLG 156 ONPHLT 177 NVAOGO 136 PYPDLV 157 YYAMCV 178 MXAXNO 137 YRPFLT 158 YYAMDW 179 NNAXQQ 138 QYPGLT 159 VXALOR 180 OOAXRR 139 MMPULY 160 VXAOLR 181 NVAVTO 140 VYAIOT 161 WXANQL 182 OWAWNT 141 WYAJTN 162 WXALQN 183 VYANOS 142 PXAONY 163 MRAYYQ 184 NVAYSO 143 PXANYO 164 MQAYRY 185 OWAYNS 144 PXAYNO 165 MPBVYY 186 WYAOSN 145 XRBCYQ 166 PMBWYY 187 POPRCY 146 XRBQYC 167 ORBIYF 188 PYPRCO 147 QXBDYR 168 QNBJYG 189 YOPPCR

4. Puzzle Description 190 CLPQRX 211 AORTWY 232 ACNOWX 191 CLPQRX 212 AORTWY 233 ADNOVX 192 DLPQRX 213 BNPQWY 234 BCQRWY 193 DLPQRX 214 BNPQWY 235 BCQRWY 194 DNPPQY 215 BNPQWY 236 BDQRVY 195 DNPPQY 216 BNPQWY 237 BDQRVY 196 DNPPQY 217 BOPRVY 238 BIOPWY 197 LPQRSY 218 BOPRVY 239 BJNPVY 198 LPQRSY 219 BOPRVY 240 LNPPQX 199 ACQRYY 220 BOPRVY 241 LOPPRX 200 ADQRYY 221 FILOPR 242 ACNQXY 201 AFNORY 222 GJLNPQ 243 ADORXY 202 AFNORY 223 ILOPPW 244 AMNOUY 203 AGNOQY 224 JLNPPV 245 BNPQXY 204 AGNOQY 225 LMPPVY 246 BNQSWY 205 AMNQXY 226 LMPPWY 247 BOPRXY 206 AMNQXY 227 LNOPSU 248 BORSVY 207 AMORXY 228 LPPQRY 249 CNOPPX 208 AMORXY 229 LPPQRY 250 DNOPPX 209 ANQTVY 230 ACIOWY 251 ANOPVY 210 ANQTVY 231 ADJNVY 252 ANOPVY 4. Puzzle Solution Clues 190 XRPCLQ 211 ORAWYT 232 WXAOCN 191 XRPQLC 212 RYAWTO 233 VXANOD 192 QXPDLR 213 NYBPWQ 234 YRBCWQ 193 QXPRLD 214 YPBQWN 235 YRBQWC 194 NPPQDY 215 PNBWYQ 236 QYBDVR 195 NYPPDQ 216 NPBQWY 237 QYBRVD 196 YPPQDN 217 YOBPVR 238 OPBIYW 197 QYPRLS 218 OPBVYR 239 PNBJYV 198 YRPQLS 219 PYBRVO 240 XPPQLN 199 RYAYCQ 220 POBRVY 241 PXPRLO 200 QYAYRD 221 ORPILF 242 NYAXCQ 201 ORANYF 222 QNPJLG 243 OYAXRD 202 RYANFO 223 OPPILW 244 MUAYNO 203 NQAOGY 224 PNPJLV 245 XPBQYN 204 QYAONG 225 MPPVLY 246 QNBWYS 205 MNAXYQ 226 PMPWLY 247 PXBRYO 206 MYAXNQ 227 ONPULS 248 ORBVYS 207 MOAXRY 228 YPPQLR 249 XOPPCN 208 MYAXRO 229 PYPRLQ 250 NXPPDO 209 NQAVTY 230 WYAOCI 251 NPAOVY 210 QYAVNT 231 VYANJD 252 PYAONV

5. Puzzle Descriptions 253 ANOPWY 274 BNOPWX 295 ANOQRV 254 ANOPWY 275 LMNPQU 296 ANOQRW 255 BMNQUY 276 LMOPRU 297 CDQQRR 256 BMORUY 277 LNPPQW 298 CDQQRR 257 ACNQWY 278 LOPPRV 299 CDQQRR 258 ACNQWY 279 ACORVY 300 CDPQRY 259 ADORVY 280 ADNQWY 301 CDPQRY 260 ADORVY 281 AMNQWY 302 CFNOPR 261 ANQQRY 282 AMORVY 303 CNOPPW 262 ANQQRY 283 BNQQRW 304 COPQRR 263 AOQRRY 284 BOQRRV 305 DGNOPQ 264 AOQRRY 285 COPQRR 306 DNOPPV 265 LNPQSW 286 DNPQQR 307 DNPQQR 266 LOPRSV 287 BMQRVY 308 FNOPRT 267 ALQRWY 288 BMQRWY 309 GNOPQT 268 ALQRVY 289 LMPQRV 310 NOPPQR 269 AMNOVX 290 LMPQRW 311 NOPPQR 270 AMNOWX 291 AINOQW 312 NOPPQR 271 ANOQRX 292 AJNORV 313 NOPQRS 272 ANOQRX 293 AMNQVY 314 NOPQRS 273 BNOPVX 294 AMORWY 5. Puzzle Solution Clues 253 OPANYW 274 NXBPWO 295 NRAOVQ 254 PYANWO 275 MNPULQ 296 OQANRW 255 MNBUYQ 276 OMPULR 297 RQQDRC 256 OMBUYR 277 PNPWLQ 298 RQCRDQ 257 NWAYCQ 278 OPPVLR 299 RQCDRQ 258 WYANQC 279 RYAOCV 300 RPQDYC 259 OVAYRD 280 QYANWD 301 PQCRDY 260 VYAODR 281 MWAYNQ 302 RNCPOF 261 NRAYQQ 282 MVAYRO 303 PNCPOW 262 RYANQQ 283 NRBQWQ 304 RPQROC 263 OQAYRR 284 QOBRVR 305 OQPDGN 264 QYAORR 285 QOPRCR 306 OPPDVN 265 QNPWLS 286 NRPQDQ 307 PQQRDN 266 ORPVLS 287 MRBVYQ 308 RNFPOT 267 QYALWR 288 QMBWYR 309 OQPGTN 268 RYALQV 289 MRPVLQ 310 PPQRON 269 NXAMVO 290 QMPWLR 311 PNQPOR 270 OXAMNW 291 NWAOIQ 312 OPPRQN 271 QXAONR 292 OVANRJ 313 RNQPOS 272 RXANQO 293 NYAMVQ 314 OQPRSN 273 XOBPVN 294 OYAMRW

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Puzzle number 305 is {D,G,N,O,P,Q}. The solution hint 305 lists the order {O, Q, P, D, G, N). Looking at the burr figure we can make the correspondence:With this correspondence, one can see from the figure where each piece goes in the solved puzzle (but not which way to flip or rotate it), and this can make it a fun, but still not too easy, to solve the puzzle. The trick for this one is to first see how the pieces must fit together when solved, and then realize that the only way to put it together is to put three together into one half, three together in the other half, and then slide the three halves together:

1 = O

2 = Q3 = P

4 = D5 = G

6 = N

Made by Interlocking Puzzles 2000.

(6.6 x 5.75 x 3.2 inch wood box with 42 wood pieces, each 3/4 x 3/4 x 2.25 inches)

35 distinct notchable 2 x 2 x 6 unit pieces, indexed with numbers in the range 0 to 56 (as shown above), a total of 42 pieces including duplicates, which can be used to assemble most of the level 5 standard 6-piece burrs. Uses David Winkler's numbering. Four puzzle and clue cards that list the pieces in order from A to F according to the diagram above.

00

01

02

03

04

05

06

07

08

09

10

19

20

21

22

23

24

25

26

28

29

30

32

33

34

35

38

39

40

44

45

46

49

53

56

Assembling a cube shape from pieces is so common it merits its own category. Most of these puzzles leave you with a bag of pieces when unassembled, but a few, such asHinged CubesandKev's Cubesare manipulation puzzles where you can pick it up, play with it, and put it down unsolved to continue later.

Copyright 1966 Piet Hein,

produced in Denmark by Skj0de of Skjern for Parker brothers, No. 1050.

(4" box with wood pieces, metal base, and instruction booklet, 3.1" assembled)

Six of the 7 pieces are formed from 4 unit size cubes and the last piece isformed from 3 unit size cubes; the goal is to assemble them into a 3x3x3 cube. This is a relatively easy puzzle with many solutions. John Rausch credits the invention of this puzzle toPiet Heinin 1936.

Further reading:

Stewart Coffin's book, from: http://www.johnrausch.com/PuzzlingWorld/chap03a.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/soma/soma.htm

Lagoon Solution, from: http://www.give-me-a-clue.com

Johnson 1988 Patent, from: www.uspto.gov - patent no. 4,784,392

Johnson 1989 Patent, from: www.uspto.gov - patent no. 4,844,466

Designed by Stuart Coffin circa 1975, made by Cubic Dissection 2002.

(6 pieces, bocote, 2.25 inches square assembled)

Here is what Coffin says inThe Puzzling World of Polyhedral Dissections:

"The six-piece version of the 3 x 3 x 3 cube will be considered first. For aesthetic reasons, one might prefer that all the pieces be the same size, but this is impossible, so the nearest approximation is to use three four-block pieces and three five-block pieces. It is also desirable that all pieces be non-symmetrical but this is likewise impossible so two of the four-block pieces will have an axis of symmetry. All pieces will of course be dissimilar. Of the several thousand such combinations possible the author tried several that proved to have either multiple solutions or no solution, until finally finding one with a unique solution."

Here is the solution hint that was sold with the puzzle:

Designed and made by Interlocking Puzzles circa 2001.

(5 pieces, 3 inches square assembled)

A similar theme, but not the same set of pieces as the 5 piece version of the 3x3x3 cube suggested by Stewart Coffin in Figure 55 ofThe Puzzling World of Polyhedral Dissections.

Designed by Stuart Coffin (circa 1975), Made by Interlocking Puzzles (circa 2001)

(4 pieces, 3 inches square assembled)

The photo on the right above shows the four pieces in their relative orientation for assembly. Here is what Coffin says inThe Puzzling World of Polyhedral Dissections:

"With puzzles of this type, there are an optimum number of pieces; and as you tinker with them, you soon gain an intuitive sense of what that number is. There is no way that a four-piece version can be very difficult, although the one shown in Fig. 51 does have the intriguing property of being serially interlocking, meaning that it can be assembled in one order only. Is a five-piece serially interlocking version possible?"

Made by AussieStuff Puzzles, purchased from Mr. Puzzle Australia, 2006.

(13 pieces, wood, 6 inches)

Thirteen pieces, each designed from unit cubes, are assembled into a 4x4x4 cube; can also be assembled into a 4 x 16 rectangle. Here is the solution that was sold with the puzzle:

Purchased from UK3, 2006.

Here is a photo of the other three sides:

Purchased from Creative Craft House 2007.

(wood, 3.1 inches)

Named because the designer's wife commented that it would take a century to solve; here are the first few steps of dissassembly:

Designed by Stewart Coffin circa 1975, made by Interlocking Puzzles 2001.

(8 pieces, maple and bloodwood, 2 inches square assembled)

The wood used to make this puzzle gives a clue to the solution with symmetric color shown above; the photos below show three basic steps to this solution:

It is not unique, here are two views of another solution:

Stewart Coffin, in his bookThe Puzzling World of Polyhedral Dissections, describes the derivation of this puzzle as starting with all possible pairs of joined 1x2x2 blocks (where the resulting 10 pieces can be assembled into a 4x4x5 solid in 25 different ways) and then eliminate the two rectangular pieces (the 1x2x4 piece and the 2x2x2 piece) to see if the remaining 8 pieces can be assembled into a cube. He then goes on to say that they cannot be so assembled, but that one can be eliminated and one duplicated to make a set that can. He also notes "an interesting pattern of symmetry" in the solution.

The 1986 patent ofGuentherdescribes puzzles where pieces are formed from pairs of rectangular solids.

Further reading:

Guenther Patent, from: www.uspto.gov - patent no. 4,534,563

"Just a Little Packing Problem #1",

made by Mr. Puzzle Australia, purchased 2006;

basic idea by Stewart Coffin circa 1975.

(8 pieces, Tasmanian Oak, 2 inches square assembled)

Like the Stewart CoffinPatio Block, puzzle, but with a slightly different set of pieces. The three photos below show basic solution steps:

Designed by Bill Cutler 1991, made by Cutler / McFarland / Peterson.

(wood, 2.5 inches)

Pieces formed from black and white unit cubes and half unit cubes (starred above) must be assembled to a 3x3x3 cube with a checkerboard pattern on all sides. The solution is unique and does not follow the checkerboard pattern in the hidden center.

Designed by V. Genel, sold by Puzzleman.com, circa 2000?

(Zebrawood and Walnut, 2+5/8 inches)

Four beautifully cut pieces ome apart in pairs:

Designed by S. Coffin 1971, made by T. Lensch 2008.

(Marblewood and Brazilian Blackwood, 2.2 inches;

sold with a piece diagrampiece diagramand anassembly diagram)

Described inCoffin's book, six identical pieces are augmented to make 6 different non-symmetric pieces, where two groups of three slide together diagonally:

Basic idea by Stewart Coffin, made by J. Storer 1989.

(purple heart with light wood dowels, 3 inches)

Stewart Coffin proposed this class of puzzle to make a 2x2x2 cube from 8 unit cubes, where each has three mutually perpendicular holes, and a total of 12 dowels are inserted into 12 of the 24 holes. He observed that the holes have one of two "reflexive forms", and that puzzles could be made by having all pieces of one form or having 4 with one and 4 with the other. The cubes of this puzzle all have the left form; the photos show basic solution steps:

Basic idea by Stewart Coffin, made by J. Storer 1989.

(top: purple heart with dowels, 3 inches;

bottom: rosewood with dowels, 2.25 inches)

Like theCubes and Pegspuzzle, except here 4 pieces have one form and 4 the other (the pattern of pegs in the soluton to this puzzle is different fromCoffin's BookFig. 193):

Designed by Ronald Kint-Bruynseels, made by Eric Fuller 2007.

(walnut box and 9 cocobolo pieces with pegs, 2.5 inches)

Nine identical 3-unit L-shaped pieces with pegs added to assemble in a unique solution to a 3x3x3 cube. Here are basic solution steps:

Patented by Andy Turner, made by Eric Fuller 2010.

(Oak box 2.75" square by 2.1" high, Bubinga puzzle 2.2" square)

Don't read any further; have some fun first. This puzzle is quite hard until one sees the trick, and then it is almost impossible to forget how to solve it.

The two 1x2 pieces have double holes at one end that naturally entices one to use them, but in fact these two faces butt against each other in the unique solution (no pegs going between them), and then the puzzle solves easily. Here are four photos in sequence of assembly:

Designed Stewart Coffin, made byInterlocking Puzzles 2000.

(7 pieces, bloodwood and aluminum, 3 inches)

There are a total of 7 pieces; 2 pieces formed from 5 unit cubes with holes and rods, 4 pieces formed from 4 unit cubes with holes and rods, and one 3 unit long rod. They must be assembled into a 3x3x3 cube (there is a unit void in the center). Stewart Coffin proposed this class of puzzles and suggested this particular selection of pieces as one that has a "satisfactory" set of two solutions. Below are two stages of a solution for which the last piece placed before the rod is the, and two stages of a solution for which the last piece placed before the rod is theT:Z

Designed Stewart Coffin; left Interlocking Puzzles 2005, right Coffin circa 1980.

(left: mahogany, eight pieces, 3.25 inches,

right: mahogany, walnut, szjo, eight pieces, 2.75 inches;

right is one of 6 puzzles purchased during a visit with the designer in the early 1980's)

Featured in a December 1991 article inFine Woodworking Magazine. Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"Special version - only one made. No half-pieces, so ignore puzzle problems that require half-pieces. The cube has only one solution in which all sides have matched wood and grain symmetry."The pieces are the eight ways to glue together a basic U-shaped piece; below are the pieces of the Interlocking puzzle version, the one made by Stewart Coffin pulled apart, and his grain pattern:

The wood and grain restriction has only one solution, but on the other hand, you are given clues how to do it. For example, there is just enough walnut to go around (a total of 8 squares), and so the solution cannot have any of the walnut squares hidden in the middle. For the single wood version, here is one of the solutions:

For the single wood version, Interlocking Puzzles said that there are 7 solutions each with a symmetric version; here is the solution sheet that was sold with the puzzle:

Designed Rick Eason 2004, purchased from Mr. Puzzle Australia 2006.

(Burdekin Plum, 2.4 inches)

The solution is unique and made more difficult due to 3 "false solutions" (arrangements that could exist in a solved state but there is no order of assembly to achieve any of them). Below are photos of two steps in the solution and the sheet that came with the puzzle:

Further reading:

Winter Patent, from: www.uspto.gov - patent no. 6,241,248

Designed by Rick Eason 2001, made by John Devost 2007.

(Bocote and Cherry, 4 pieces, 2.4 inches square;

as described onRick Eason's Page, this puzzle was also mass produced as

"Confusion Puzzle Mental Block" shown on the right above - wood 2.9" square)

Four pieces formed from unit cubes and rods of dimensions 1/2 by 1/2 by 2.5 units.

The photos below show the four pieces positioned to be assembled, and pairs put together; the final step slides these two halves together to get the solved cube shown above.

Further Reading

Rick Eason's Page, from: http://www.mechanicalpuzzles.org/puzzles/index.html

Amazon: http://www.amazon.co.uk/Lagoon-CONFUSION-PUZZLE-MENTAL-BLOCK/dp/B004KYNB76

Designed by Kevin Holmes and Rik Van Grol, made by Eric Fuller 2009.

(Peruvian Walnut and Spalted Oak, 2.7 inches)

A beautiful and fun puzzle; here are photos of assembly:

a.k.a.Magic Cube

Circa 2000.

(laminated cardboard with Andy Warhol art, 2.75 inches)

Unlike theHinged Cubespuzzle, this puzzle is trivial to solve and is more of a toy than a puzzle. The cube shown above, can be unfolded in two different ways to form a 2 x 4 array, and then in both cases that 2 x 4 array can be folded lengthwise to form another 2 x 4 array:

Copyright James A. Storer 2009; U.S. patent 8,393,623 March 2013.

(Kingwood with brass hinges, 2.25 inches square assembled)

Fold the eight cubes into a larger 2x2x2 cube; there are 7 hinges:

Hinge 1 joins cube 2 to cube 1, on the front faces.

Hinge 2 joins cube 3 to cube 2, on the back face of 3 and the right face of 2.

Hinge 3 joins cube 4 to cube 3, on the top faces.

Hinge 4 joins cube 5 to cube 4, on the front faces.

Hinge 5 joins cube 6 to cube 5, on the left face of 6 and the right face of 5.

Hinge 6 joins cube 7 to cube 6, on the back face of 7 and the front face of 6.

Hinge 7 joins cube 8 to cube 6, on the top faces.

A fun but not too hard puzzle; when left on a coffee table, people often spend 30 minutes or so to solve it (about right for a coffee table audience). Not only is there something very satisfying about the solid feel of real hinges, but they also tend to suggest a straightforward folding one cube at a time, which inevitably leads to a position like the one shown on the right above.

a.k.a.Snake Cubes, Serpent Cubes, Cubra Cubes

Designed by Trench Puzzles circa 1985, made by Jim Storer 1988.

(bloodwood, 2.8 inches assembled)

Twenty seven cubes are threaded together with an elastic cord to form a "snake" that can be folded up by rotating adjacent cubes with respect to each other; the object is to form a 3 by 3 by 3 cube (where none of the elastic cord shows).

Many puzzles are possible by threading different patterns. If you imagine the cubes alternately colored red, black, red, ..., then the solved 3x3x3 cube will have red cubes at the corners and the face centers. The Kev pattern is has a unique solution where the snake ends are face centers.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/snakecube.htm

Mark Weston's Page, from: http://www.cs.uvic.ca/~mweston/snakes.html

Eryk Vershen's Page; from: http://cantaforda.com/cfcl/eryk/puzzles/chain_cube.html

Dreyer Patent, from: www.uspto.gov - patent no. 3,222,072

a.k.a.Snake Cubes, Serpent Cubes

Same idea as Kev's Snake Cubes, but a different pattern.

(2 inches square)

The Cubra Cubes are the same idea as Kev's Snake Cubes, but come in a number of different patterns; this is the first pattern shown onMark Weston's Page:"A solution can be described by a string of "directions" that the cube follows when you wrap it into a cube, either Right, Left, Up, Down, Forward, or Back. So for example if a solution starts R R F L ... then put the end of the snake with the rest trailing off to the Right, then the next cube goes in the same direction (it must be a straight-through cube), the next cube (a corner cube) turns to point Forward, then it goes Left, etc."Unlike Kev's Cubes, a solution starts and ends in the corners, and is not unique. Here is a solution that is provided for the

Solutions:

R R F L U U F D D R U B B L L F D F U U B B R R F F

R R U L F F U B B R F D D L L U B U F F D D R R U U"Lagoonversion of this puzzle (the same as the first one above, with the directions R-L, F-B, U-D all reversed):

Further reading:

Mark Weston's Page, from: http://www.cs.uvic.ca/~mweston/snakes.html

Lagoon Solution, from: http://www.give-me-a-clue.com

Packing puzzles typically require one to fit pieces into a tray (two dimensional) or a box (three dimensional), although sometimes the problem is to fit the pieces into a particular shape. Perhaps the most well known example, which as been around for centuries, is thetangram, where the goal is to use the same set of simple two dimensional shapes to make many different shapes.

a.k.a.All Square Novelty Puzzle, Check-A-Board, Tyr & Do It,

Famous Checkerboard Puzzle, Weekly Telegraph Chessboard Puzzle

Left: Made 1940's by a relative of J. A. Storer who lived in up-state New York.

(wood cigar box and painted pieces cut from 1/4" masonite, with 1" squares)

Right two: J. F. Friedel Co., Syracuse, N.Y, circa 1940's.

(6.5 by 8 by 1" cardboard box and 12 cardboard pieces with 1+3/8" squares;

top edge says "Mfg. by J. F. FREDEL CO. Syracuse N.Y.";

bottom edge says "MFGS. REPRESENTATIVES POTTER & REAGAN")

Arrange the pieces to make a standard 8 by 8 checkerboard. There are 10 distinct pieces and two of the 5-unit Z's. Shown on pages 70-73 of theHaubrich book, which lists a unique solution (shown above). Here is another version made in Great Britian:

All Square Novelty Puzzle, Frederick Warne & Co.,

London and NY, circa 1930's?

(6.25 x 6.25 x 13/16 inch cardboard box

and 12 wood pieces based on 15/16" squares 1/8 inch thick;

directions on the back of the box)

Note: Frederick Warne & Co. is the publisher of

the 1893Hoffmann book.

Patented by H. Luers and made by Selchow & Righter, NY, circa 1880.

(8.5 inches square by 3/4 inch cardboard box and 15 cardboard pieces, 14 distinct;

pieces based on 1 inch squares can be arranged in the box;

on the cover and pages 217-219 of theHaubrich book,

which lists this puzzle having 6,013 solutions;

solution on the left above is from Haubrich, and right is from the Luers patent)

Left is a solution a previous owner drew inside the box bottom, right is the label on the box top, and below is the label inside the box top.

This version is nearly identical to the one shown on the previous pages, except the color of the label on the box top is a bit more brown than gray, and the pattern around the edge is a bit different (and this one has nothing inside the box top or bottom).

Phenyo-Caffein Co., Worcester, MA, circa 1900.

(5.25 inches square by 5/8 inch cardboard box and 15 cardboard pieces, 14 distinct;

pieces based on 5/8 inch squares can be arranged in the box;

also made with a wood box of the same dimensons and graphics)

The Pheno-Caffein Co. also made theMisfit 6 Piece Burr. The inside of the box bottom (on the right above) challenges the solver by stating that the dark square of the smallest piece can occupy any of the 32 dark squares. The sheet available from the company, on the next page, shows eight solutions (representing solution classes).

Further Reading

Luers Patent, from: www.uspto.gov - patent no. 231,963

a.k.a.Famous 'Bug House' Puzzle

Feltham Co., London, Royal Letters Patent 16,310, circa 1889.

(cardboard box and 14 thick cardboard pieces, 5" x 5" x 1/2";

box bottom has add for Feltham's tennis bat;

has a sheet that is the same as what is on the inside of the box bottom;

shown on pages 165-174 of theHaubrich book,

which gives the date and lists this puzzle as having 84 solutions; one is shown above)

Franco, NY, circa 1948.

(cardboard box and 14 distinct metal pieces, 3.25" x 3.25" x 1/2")

The Bug House Puzzle, E.I.H. Co. and F&K, 1912.

(cardboard box and 14 distinct metal pieces, 2.1 by 3.1 by 1/2 inches;

inside box top gives directions and manufacture;

shown on the cover and on pages 150-151 of theHaubrich book,

which gives the manufacture date,

identifies "E. I. Horsman Co." and "Forsheim & Koningsberg", NY,

and lists this puzzle as having 141 solutions, one of which is shown below)

Note:There were a number of variations of this puzzle made. This one is the same as page 150-151 of the Haubrich book if the pieces with dots in the photo above are taken to be black; however, the dots shown in the Haubrich book are not in the same locations.

Vasen Mfg. Co., Davenport, Iowa, 1928.

(cardboard box and 14 distinct cardboard pieces, 4.25 by 4.25 by 5/8 inches;

inside box bottom says you can send 10 cents to get three different solutions;

shown on pages 158-164 of theHaubrich book,

which lists this puzzle as having 84 solutions, one of which is shown above)

Note:Pages 165-174 of the Haubrich book show puzzles that are the same except for the colors reversed, and pages 183-187 of the Haubrich book include the same box top where if the pieces for those puzzles have the colors reversed, they are the same except for one (and the same asXcel Checkerboard Puzzle No. 1).

Doyle Puzzle Co., Buffalo, NY, circa 1920?

(cardboard box 5.1"x5.1"x7/8", and 14 distinct cardboard pieces with 3/4" squares;

same as theFamous and Baffling Checkerboard Puzzlewith colors reversed;

also made in a 13 piece version, theNew XceL Checkerboard Puzzle No. 2;

shown on pages 183-187 of theHaubrich book,

which lists this puzzle as having 84 solutions, one of which is shown below)

Note: TheChequers Puzzleshown on page 97 of the1893 Hoffmann Bookis the same as a mirror image of this puzzle, except that puzzle shows only 63 squares, and can be corrected to make one of the three 4-unit L's be a 5-unit Z.

Doyle Puzzle Co., Buffalo, NY, circa 1920?

(cardboard box 5.1"x5.1"x7/8", and 13 distinct cardboard pieces with 3/4" squares;

also made in a 14 piece version, theXceL Checkerboard Puzzle No. 1;

shown on page 122 of theHaubrich book,

which lists this puzzle as having 7 solutions,

5 of which a composed of two 4 by 8 solutions,

one of these 5 and one other are shown below,

where the black squares correspond to green and the white to black)

Gyro Checker Board Jig Saw Puzzle, undated.

(3.5 by 6 inch envelope and 14 distinct cardboard pieces based on 1 inch squares;

shown on page 196 of theHaubrich book,

which lists this puzzle as having 598 solutions, one of which is shown below)

a.k.a.Krazee Checkerboard Puzzle, Zebas Puzzle,

Banzee Island Checkerboard Puzzle, 59-444 Checkerboard Puzzle

Peter Pan Playthings, England, circa 1950.

(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;

there are 11 distinct pieces, where there are two of the 6-unit L;

shown on pages 57-65 of theHaubrich book, which gives the manufacture date

and list this puzzle as having 11 solutions, one of which is shown above;

pages 60-65 show reflected with reverse colors patented by J. Avila-Valdez 1995)

Arrange the pieces to make a standard 8 by 8 checkerboard. Paper, shown below, is glued to the bottom inside of the box that gives a layout for quickly storing the pieces unsolved in the box. The bottom of the box is a non-transparent black plastic that does not allow you to see the back of the paper. However, by holding it up to the light one can see that the reverse side of the paper has instructions similar to theKrazee Checkerboard Puzzle, shown on the following page.

Further Reading

Avila-Valdez Patent, from: www.uspto.gov - patent no. 5,403,005

Krazee Checkerboard Puzzle, Plas-Trix Co., Jamica, NY, 1957.

(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;

same puzzle as theDraught Checkerboard Puzzleshown on the previous page,

but the back of the box is clear to allow one to view directions;

also shown on pages 57-58 of theHaubrich book, which gives the manufacture date)

Zebas Checkerboard Puzzle, Plas-Trix Co., Brooklyn, NY.

(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;

same puzzle as theKrazee Checkerboard Puzzleshown on the previous page,

and also made by the Plas-Trix Co., but with different packaging)

Banzee Island Checkerboard Puzzle, made in Hong Kong.

(12 plastic pieces in plastic bag with cardboard top, 6.25 by 6.5 inches;

same puzzle as the Zebas Checkerboard Puzzle shown above,

the back of the package top refers to Chief Zebas)

S. Adams Co. Neptune, NJ., Copyright 1958.

(6" by 4" cardboard package and six 3.5 by 2.5 inch puzzles,

the checkerboard and five others, including Magic T;

shown on page 167 of theAdams Co. History book;

shown on page 21 of theHaubrich book.

which presents the unique solution shown above)

Made in Japan circa 1940.

(wood box 3.8 by 3.75 by 7/16 inches thick and 19 wood pieces;

wood inlays on the box cover are 5/8 inch diameter;

paper stamp on the back is 1/2 inch square)

Purchased from someone who remembered it from his childhood in the 1940's. At some point in the past the following solution was drawn:

This puzzle has the same dimensions, style, and cover inlays as the 16 piece puzzle on page 233 of theHaubrich book. However, even if one assumes that the 1x1 pieces broke off of larger ones before the solution above was drawn, and taking into account rotations and reflections (the pieces are double sided), there is no way to make it the same (and no way to further combine pieces to make it the same as the 14 piece puzzle of the same style on page 177) Here are the 16 pieces if the 1x1's are joined to the pieces above them in the solution above:

a.k.a.Caricature, Cut-Up Square, Stone Tangram,

Union Stone Puzzle, Richter Anchor Stone Puzzle No. 8

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3.1" x 3.1" x 9/16", 7 stone pieces, booklet, and solution booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1890;

described on pages 77-79, 96-97, 111-115, 128 of the 1893Hoffmann book.

"casse tete" and "kopfzerbrecher" mean headache in French and German;

inside of the cover shows how to pack the pieces into the box;

inside of the box bottom has an add for "Dr. Richter's Pain-Expeller";

booklet has multi-language text inside covers and on pages A to Q at the front,

and 64 pages with 195 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle;

second booklet has solutions)

An old design known as theTangram, dating back to ancient China; seven tiles, calledTans, can be used to make different shapes. TheRichter Companyof Germany, known for stone building blocks, started making this puzzle and others in 1891. It is number 8 of over 36; seeThe Anchor Puzzle Book,The Tangram Book,Slocum and Botermans books, and also theRichter Summarylater in these pages. Many versions of the tangram have been made, some packaged as two squares of half the area:

Richter (1846-1910) had a number of business besides stone building sets and puzzles, including selling medicines (see the Richter history on the Ankerstein Page). Many of the Richter puzzles have adds or testimonials to his pain medicine. The add below is on the inside of the box bottom of the puzzle on the preceding page.

The text on pages A to Q at the start of the booklet that precedes the 64 pages of shapes is very similar to that in versions of a number of other Richter puzzles (e.g., see the corresponding pages for theTormentorandPythagoraspuzzles). Page L describes how the last 16 pages are shapes made in combination with another puzzle; shapes 180 to 183 use theCircular Puzzle, shapes 184 to 187 use theTormentor, shapes 188 to 191 use theCross Puzzle, and shapes 192 to 195 usePythagoras. An English description similar to what is on Page L is given in the description that came with the "Puzzle Drive" version shown below.

These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 195) is shown with page 1 (patterns 1 through 4).Note:

This figure was extracted from the page scans shown on the preceding page; the patterns are in the order as in the booklet (left to right, top to bottom), except that page 64 (shape 195) is shown with page 1 (shapes 1 through 4).

The shapes on the first 48 pages need only the pieces of this puzzle. This figure was cropped from the figure of all shapes on the preceding page; the patterns are in the order as in the booklet (left to right, top to bottom), except that the last 4 patterns (page 48) are at the end of row 1.

(cardboard box 3.2 by 3.2 by 5/8 inches, 7 stone pieces, and two booklets;

the inside of the cover shows how to pack the pieces into the box;

box is constructed with a lip on the bottom,

booklet cover says "The Anchor Puzzle 3rd Ed",

booklet inside cover for "Casse-Tete Persan" and cover for "Kopfzerbrecher",

which says that this is the "third edition" at a price of "15 kr.",

is followed by a 3 page French and German introduction,

followed by unnumbered pages of shapes similar to the puzzle on the first page,

followed by a final page, in German, that advertizes Anchor blocks

by referring to the picture on the back of the booklet;

second booklet is a work book with shapes to draw in and many blank pages)

(cardboard box 3 by 3 by 9/16 inches, 7 stone pieces, and two booklets;

similar to the version on the previous page;

a more compact box where the small bottom lip is hidden when the cover is on;

box top graphics and booklet front and back (shown above) are the same;

inside box bottom advertizes "ANCHOR PAIN EXPELLER" from 1890;

booklet is basically the same except it is in German and English;

booklet inside cover for for "Kopfzerbrecher" and "The Anchor Puzzle",

which says that this is the "third edition" at a price of "10 cents",

followed by a 3 page German and English introduction,

followed by unnumbered pages of shapes similar to the puzzle on the first page,

folloed by a final page, in English, that advertizes Anchor blocks

by refering to the picture on the back of the booklet)

(cardboard box 3.1 by 3.1 by 1/2 inches, 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

box bottom lists other puzzles for sale,

the booklet has 64 pages of the same 195 shapes as the puzzle on the first page,

along with the single loose double sided page of English directions shown above)

some versions have the same box cover with "UNION" instead of "ANCHOR"

and the same booklet cover with just "STONE PUZZLE" on a single line)

(cardboard box 3.1 by 3.1 by 5/8 inches, 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

box and booklet front show copyright, and booklet back shows the U.S. manufacturer;

the booklet has text on the insides of the covers and 48 pages

of the same 179 shapes as the first 48 pages of shapes on the first page;

unlike earlier versions of this puzzle, an explicit copyright date is shown)

(cardboard box 3.1 by 3.1 by 9/16 inches, 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

the booklet has 64 pages of the same 195 shapes as the puzzle on the first page,

however its cover is blank, and there is no text explaining that

the last 16 pages are shapes made in combination with another puzzle;

the pages of this booklet were used for the scans shown earlier)

a.k.a.All Nine, Richter Anchor Stone Puzzle No. 1

F. Ad. Richter & Co., Germany, late 1890's / early 1900's

(cardboard box 2.7" x 4.4" x 1/2", 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1899;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 141 shapes to make,

the first of which is the star, which can be solved as shown above,

and where the last 16 pages are shapes made in combination with another puzzle)

(cardboard box 2.7" x 4.4" x 1/2", 9 stone pieces, and booklet;

booklet has the same shape pages as the one on the previous page,

but no additional text pages;

back of the box lists other puzzles)

a.k.a.Richter Anchor Stone Puzzle No. 2

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3.1" x 3.6" x 9/16", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1893;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 140 shapes to make;

where the last 16 pages are shapes made in combination with another puzzle;

the first four shapes are the rectangle, parallogram, triangle, and hexagon)

Same size box and booklet as version on the preceding page.

The booklet starts with 16 not numbered pages, where the first 12 are a page of directions in 12 different languages, and the last 4 pages have multi-language text with a coupon that could be mailed in along with 15 cents to get solutions to all of the problems. Following these 16 pages are 48 pages of the same problems as the version on the preceding page. The booklet front cover, inside of the front cover, inside of the back cover, and the back, present the same text in 12 different languages; on the inside of the back cover, the English text says "Second book to The "Lightning Conductor" for drawing in the lines of solved problems." So it would appear to be the second of two booklets that originally came with the puzzle.

Same size box and booklet as version on the preceding pages.

The booklet has 48 pages of the same problems as the version on the preceding pages.

(cardboard box 3.1" x 3.7" x 1/2", 7 stone pieces, and booklet;

German text on inside of front and back cover;

also has a loose sheet with directions in German;

same 48 pages with 140 shapes to make as puzzle on first page)

(same pieces but different shapes thanRichter 16 Magic Egg)

a.k.a.a.k.a. Columbus' Egg, Columbian Puzzle, Richter Anchor Stone Puzzle No. 3

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1893;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 111 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle;

there are no graphics on the back of the booklet)

(cardboard box 3.1" x 4.1" x 1/2" with wood inserts, 9 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

the booklet has multi-language text inside the covers and on pages A to Q at the front,

and 32 pages with 95 shapes to make;

the booklet is the same as the one on the preceding page

except without the final 16 pages)

(cardboard box 4" x 3.5" x 5/8" with cardboard insert, 9 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

booklet has Spanish and Hungarian inside the front cover and German inside the back cover,

and at the front are 3 pages of Spanish directions and 4 pages of Hungarian directions,

48 pages present the same pages as the puzzle on the first page,

where the figures have a shaded green texture as shown above)

a.k.a.Richter Anchor Stone Puzzle No. 4

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 4.1" x 3.1" x 9/16", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1896;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 130 shapes to make,

where the directions state that the first is the square using only 6 pieces,

the second is the right triangle of 3/2 the height of the square using only 7 pieces,

all others use all eight pieces,

and where the last 16 pages are shapes made in combination with another puzzle)

(cardboard box 3.1" x 4.1" x 1/2", 8 stone pieces, and booklet;

similar booklet with the same shapes as the version on the previous page)

(cardboard box 3.25" x 4.1" x 9/16", 8 stone pieces, and booklet;

same problem pages as the versions on the preceding pages,

but with no front or back matter, except for a loose double sided page

tucked under the cover - front and back shown above)

a.k.a.Richter Anchor Stone Puzzle No. 5

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1893;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 108 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle)

(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text on pages A to Q at the front,

and 48 pages with the same 108 shapes to make as the puzzle on the preceding page)--- 242 --- Trouble Killer, Continued

(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

this one is missing the booklet;

it came with some extra cardboard pieces

that are in the bottom of the box below the stone pieces)

a.k.a.Richter Anchor Stone Puzzle No. 6

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 3.5" x 3.5" x 9/16", 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1911;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 32 pages with 98 shapes to make;

the text above is on the box bottom under the puzzle)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.5" x 3.5" x 9/16", 9 stone pieces, and booklet;

booklet has the same 32 pages with 98 shapes to make

as the puzzle of the first page, but no additional text;

included is one loose double sided page of text)

a.k.a.Goblin, Richter Anchor Stone Puzzle No. 7

F. Ad. Richter & Co., Germany, late 1890's / early 1900's

(cardboard box 3" x 4" x 9/16", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1899;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 143 shapes to make;

where the last 16 pages are shapes made in combination with another puzzle;

a previous owner has penceled in a solution to the first problem shown above)

a.k.a.Richter Anchor Stone Puzzle No. 9

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3.6" x 3.6" x 9/16", 10 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1891;

described on pages 85-87, 120-121 of the 1893Hoffmann book;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 121 shapes to make;

where the last 16 pages are shapes made in combination with another puzzle)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.6" x 3.6" x 9/16", 10 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

the booklet starts with 8 pages of multi-language text,

followed by 48 pages of the same 121 shapes as the puzzle on the first page;

this box top was made with a number of variationsabof the text for different markets)

Richter Co., circa 1890's / early 1900's.

(cardboard box 3.7" x 3.7" x 9/16", 10 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

box bottom lists other puzzles for sale,

booklet has 48 pages of the same 121 shapes as the puzzle on the first page,

along with the single loose double sided page of English directions shown above)

a.k.a.Sherlock Holmes, Hi Ho, Richter Anchor Stone Puzzle No. 10

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3" x 3.75" x 9/16", 7 stone pieces, and two booklets;

theAnchor Puzzle Bookdates this puzzle as first made in 1892;

described on page 83-85, 118-119 of theHoffmann book;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the inside of the bottom has a testimonial dated 1899,

variationsof this testimonial appear in the box top or bottom other versions;

first booklet has multi-language text inside covers and on pages A to Q at the front,

and 48 pages with 149 shapes to make

the first of which is the cross as shown above,

and where the last 16 pages are shapes made in combination with another puzzle;

the second booklet gives a solution for each shape)

Same dimensions as version on the first page;

the inside of the cover shows how to pack the pieces into the box;

booklet has nothing on the inside covers,

with 8 unnumbered pages of multi-language text,

followed by the same 48 pages of problems as the version on the first page;

the first page credits Dr. Richter's Publishing House, 215 Pearl St., NY;

second booklet is the same solution booklet as the one on the first page.

Same dimensions as version on the first page;

box construction uses a lip on the bottom;

the inside of the cover shows how to pack the pieces into the box;

inside of the bottom has a testimonial dated 1890;

inside covers and first 8 unnumbered pages have multi-language text,

followed by 48 pages with the same problems as the version on the first page;

however, the problems are drawn with black line art rather than red coloring;

the first page of problems is shown to the right of the booklet cover above;

second booklet has solutions for problems on the first 32 pages.

Note:Version shown on the top right is Dutch version; it says "Kruisraadsel" at the bottom of the box top and on the front cover of the booklet (which has the identical pages).

Same puzzle as the one shown on the first page;

3" x 3.7" x 1/2";

booklet has the same 48 shapes to make,

but without the text pages at the front and back.

a.k.a.Richter Anchor Stone Puzzle No. 11

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3.1" x 3.1" x 5/8", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1894;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has 8 pages of multi-language text at the beginning,

and 32 pages with 89 shapes to make)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.1" x 3.1" x 9/16", 8 stone pieces,

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside covers and on pages A to Q at the front,

and 32 pages with 89 shapes to make, same as those on the preceding page)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.1" x 3.1" x 5/8", 8 stone pieces,

and booklet of 32 pages with the same 89 shapes as the preceding page)

a.k.a.a.k.a. Richter Anchor Stone Puzzle No. 12

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3 by 3 by 9/16 inches, 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1891;

described on pages 81-83, 117-118 of the 1893Hoffmann book;

similar in construction to theAnchor Puzzle Tangram;

the inside of the box cover shows how to pack the pieces into the box;

the inside of the box bottom has a testimonial dated 1899;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 64 pages of 197 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle)

Described on page L of the booklet, the last 16 pages are shapes made in combination with another puzzle; shapes 182 to 185 use theAnchor Puzzle, shapes 186 to 189 use theTormentor, shapes 190 to 193 use theCircular Puzzle, and shapes 194 to 197 use theCross Puzzle.

These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 197) is shown with page 1 (patterns 1 through 3).Note:

Here are the front and back cover, the inside front cover, pages A through Q that come before the problem pages, and the inside back cover. The text in German, French, and English discusses this and other puzzles, and gives testimony from a satisfied customer.

Similar to the version on the first page, but

box has different construction with a lip on the bottom,

booklet has multi-language text on inside covers and 6 unnumbered pages,

and the booklet has the same problems but drawn with black and white art

(first three pages of problems shown above)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.1 by 3.1 by 1/2 inches, 8 stone pieces, and booklet;

the inside of the box cover shows how to pack the pieces into the box;

the booklet has the same 64 pages with 197 shapes to make as the puzzle on the first page,

where the last 16 pages are shapes made in combination with another puzzle,

and the extra double-sided sheet describes them)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3 by 3 by 1/2 inches, 8 stone pieces, and booklet;

the cover slides on;

the booklet is 48 pages of 181 puzzles;

these 48 pages are the same as the first 48 pages of the puzzle on the first page;

there is an extra double-sided text page in German between pages 18 and 19,

that seems to be a bit out of place because it discusses

the combinations that would be on the other 16 pages)

a.k.a.Richter Anchor Stone Puzzle 13

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3 by 3 by 9/16 inches, 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1891;

described on pages 80-81 of the 1893Hoffmann book;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the inside of the bottom has a testimonial dated 1899;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 64 pages with 174 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle)

Described on page L of the booklet, the last 16 pages are shapes made in combination with another puzzle; shapes 159 to 162 use theCircular Puzzle, shapes 163 to 166 use theAnchor Puzzle, shapes 167 to 170 use theCross Puzzle, and shapes 171 to 174 usePythagoras.

These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 174) is shown with page 1 (patterns 1 through 4).Note:

Here are the front and back cover, the inside front cover, pages A through Q that come before the problem pages, and the inside back cover. The text in German, French, and English discusses this and other puzzles, and gives testimony from a satisfied customer.

Same as the version on the first page

except for the art on the box top and the front and back of the booklet

(same box top inside, testimonial, booklet text and problems).

Similar to the version above, but

box has different construction with a lip on the bottom,

booklet has multi-language text on inside covers and 8 unnumbered pages,

and the booklet has the same problems but drawn with black and white art;

the first three pages of problems are shown above.

(cardboard box 3.1 by 3.1 by 1/2 inches, 8 stone pieces, and booklet;

inside of the box cover shows how to pack the pieces into the box;

booklet has the same 64 pages with 174 shapes as the puzzle shown on the first page,

where the two sided instruction sheet describes the puzzle)

a.k.a.Richter Anchor Stone Puzzle No. 14 (sometimes 3)

F. Ad. Richter & Co., Germany, late 1890's / early 1900's

(cardboard box 3" x 3+7/8" x 1/2", 10 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1899;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has 48 pages with 136 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle;

the solution to the first problem in the booklet is shown above)

Note:Although usually referred to with the number 14, some versions of the box graphics showed the number 3.

a.k.a.Richter Anchor Stone Puzzle No. 14 /3

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3" x 3+78" x 1/2", 10 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

booklet has 48 pages with the same 136 shapes to make as the preceding page)

a.k.a.Richter Anchor Stone Puzzle No. 14 /3

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3" x 3+78" x 1/2", 10 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

booklet has 48 pages with the same 136 shapes to make as the preceding pages)

a.k.a.Lott's Stone Puzzle, Anchor Puzzle No. 15 (sometimes 16)

F. Ad. Richter & Co., Germany, late 1890's / early 1900's

(cardboard box 2.7" x 4.4" x 9/16", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1899;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

a second way of packing the pieces into the box is shown by the figure above;

the inside of the bottom has a testimonial dated 1899;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 135 shapes to make,

the first of which is the pyramid of square root 3 times the height of the rectangle,

and where the last 16 pages are shapes made in combination with another puzzle;

Note:The box above does not show a number. However this puzzle was commonly listed by in Richter literature as number 15, and 15 appears on the boxes of some versions. It was also made with a box that has the same graphics as the one above with "No. 16." above the word Sphinx.

Puzzle pieces the same as the first page but box is 2.75" x 4.9" x 1/2";

booklet has the same 48 pages of problems but no additional text;

the inside of the cover shows how to pack the pieces into the box;

directions are on a separate two sided sheet that is slightly smaller than booklet pages.

Puzzle pieces the same as the first page;

booklet has the same 48 pages of problems but no additional text;

the inside of the cover shows how to pack the pieces into the box;

directions are on a separate two sided sheet that is slightly smaller than booklet pages.

"Lott's Stone Puzzle", copyright 1911, Lott's Bricks, LTD, Watford, England.

(cardboard box 2.7" x 4.2" x 9/16", 7 stone pieces, and booklet;

the booklet pages 1 and 2 are an introduction,

the last page invites one to write for a solution to another puzzle,

and pages 3 through 31 show 105 shapes to make,

where page 31 shows the rectangle for how to pack the pieces into the box)

(same pieces but different shapes thanRichter 3 Egg Of Columbus)

a.k.a.Miracle Egg, Richter Anchor Stone Puzzle No. 16 (sometimes 17)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1912;

booklet has 48 pages with the same 106 shapes to make

as the puzzle on the following page, but without the other pages of text)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;

also made with the similar box top but without "No. 17",

the inside of the cover shows how to pack the pieces into the box;

the booklet has multi-language text inside the covers and on pages A to Y at the front,

and 48 pages with the same 106 shapes to make as puzzle in preceding page;

the first page of shapes has written "Copyright Nachdruck verboten";

all shapes use only the 9 pieces of the puzzle;

the booklet names each shape in pages A to Y)

a.k.a.Richter Anchor Puzzle No. 17

F. Ad. Richter & Co., Germany, 1890's / early 1900's

(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1893;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside the covers and on pages A to Q at the front,

and 48 pages with 113 shapes to make,

where the last 16 pages are shapes made in combination with another puzzle)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text on eight unumbered pages at the front,

and 48 pages with the same 113 shapes to make as the puzzle on the previous page,

where the last 16 pages are shapes made in combination with another puzzle;

this Gnome theme box top was made with differentvariationsof the text)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

the booklet has the same 48 pages with 113 shapes to make

as the puzzle on the first page, but with no additional directions)

Richter & Co., Germany, circa 1890's / early 1900's.

(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;

the inside of the cover shows how to pack the pieces into the box;

the booklet has the same 48 pages with 113 shapes to make

as the puzzle on the first page, but with no additional directions);

two addition directions sheets are included)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 3.2" x 4.3" x 9/16", 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

booklet has multi-language text inside covers and on pages I to XIX at front,

where none of the text is in English,

followed by a blank page where a previous owner has drawn

a solution to the additional shape shown above,

followed by 32 pages with 97 shapes to make)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.25" x 4.25" x 1/2", 7 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 99 shapes to make,

where the first is the rectangle for the box packing

and next three are the parallelogram, square, and triangle shown above)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.75" x 3.7" x 1/2", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 98 shapes to make,

where the first is the rectangle for the box packing

and the second is the parallelogram shown above)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2+11/16" x 4.25" x 1/2", 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 96 shapes to make,

where the first is the shape for the box packing

and the second is the rectangle shown above)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.5" x 4.5" x 1/2", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 96 shapes to make,

where the first is the rectangle for the box packing

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.75" x 3.7" x 1/2", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 98 shapes to make,

where the first is the rectangle for the box packing

and the second is the parallelogram shown above)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.75" x 3.7" x 1/2", 9 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 96 shapes to make,

where the first is the rectangle for the box packing

and the second is the octagon shown above)

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 3.1" x 3.75" x 1/2", 8 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1917;

similar in construction to theAnchor Puzzle Tangram;

the inside of the cover shows how to pack the pieces into the box;

the booklet has English text on the inside of the covers shown above,

and 32 pages with 96 shapes to make,

where the first is the rectangle for the box packing

and the second is the shape shown above;

label across front is from F. A. O. Swartz, N.Y.)

The manufacture for theRichter Anchor Puzzlesbegan in the 1890's, where the puzzles numbered above 17 were made in the World War I era. The 1893Hoffmann bookdescribes theAnchor,Circular,Cross,Pythagoras, andTormentorpuzzles (and also theStar Puzzle). A history of the Richter puzzles is presented inThe Anchor Puzzle Bookby Jerry Slocum (see also theSlocum and Botermans books). The puzzle boxes were made with a variety of cover art (see the following page), although the stone pieces, made with the Richter Co. patented process, are the same. Perhaps what made these puzzles so popular were the fun booklets that came with them, giving a host of shapes to make.

Here is a booklet that came with theAnchor Puzzle, and also a corresponding solution booklet that one could purchase by mail:

Generally, booklets have more or less the same cover art as the box top, but not always. For example, on the left and middle are booklets for versions of theTormentorandCross Puzzlethat look very different from the corresponding box top, and on the right is a booklet for a version of theAnchor Puzzlethat has blank covers (and nothing inside besides the problem figures):

Here are two examples of additional work booklets that came with theAnchorandLightning Conductorpuzzles:

Some box themes were highly regular; here are some examples (the last one in the first row is used on boxes numbered above 17, and the others for 17 and below, where the last three in the second row are dated in theThe Anchor Puzzle Bookas relatively late versions first made in 1922, 1925, and 1932 respectively):

Other themes used fun graphics (e.g., people thinking, specialized graphics, cartoons); here are some examples (all used on puzzles numbered 17 and below):

Richter 1

"The Nine"

Richter 2

"Lightning Conductor"

Richter 3

"Egg Of Columbus"

Richter 4

"Patience Prover"

Richter 5

"Trouble Killer"

Richter 6

"Heart Puzzle"

Richter 7

"Kobold"

Richter 8

"Anchor Puzzle"

Richter 9

"Circular Puzzle"

Richter 10

"Cross Puzzle"

Richter 11

"Not Too Hasty"

Richter 12

"Pythagoras"

Richter 13

"Tormentor"

Richter 14

"Be Quiet"

Richter 15

"Sphinx"

Richter 16

"Magic Egg"

Richter 17

"Wrath Breaker"

Richter 18

"Archimedes"

Richter 19

"Ende Gut, Alles Gut"

Richter 20

"Pass Auf"

Richter 21

"Eile mit Weile"

Richter 22

"Sorenbrecher"

Richter 23

"Kopernikus"

Richter 24

"Pyramide"

Richter 25

"Nur Mut"

Richter 26

"Bose Siben"

Richter 27

"Ritze Ratze"

Richter 28

"Frisch Gewagt"

Richter 29

"Zeitvertreiber"

Richter 30

"Zeppelin"

Richter 31

"Kiebitz-Ei"

Richter 32

"Wer Wegt Gewinnt"

Richter 33

"Fur Kluge Leute"

Richter 34

"Hexenmeister"

Richter 35

"Teufeldien"

Richter 36

"Heureka"

Here are pages from an old Richter Brochure (courtesy of Jerry Slocum,Puzzles Old And New, Copyright 1986, page 28); see alsoThe Anchor Puzzle Bookby Jerry Slocum.

Here (and on the following page) are the shapes used to make the 36 Richter Anchor Puzzles (courtesy of Jerry Slocum,Puzzles Old And New, Copyright 1986, page 28); see alsoThe Anchor Puzzle Bookby Jerry Slocum.

(second half of the figure fromPuzzles Old And New, Copyright 1986, page 28)

The Anchor Puzzle Book, from: http://www.SlocumPuzzles.com

Richter Company U.S. Brochure, from: http://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzRichterBrochure.html

Anker Page, from: http://www.ankerstein.org

Richter History, from: http://www.ankerstein.org/html/CO.HTM

Wikipedia Tangram Page, from: http://en.wikipedia.org/wiki/Tangram

Rubiks.com Double Tangram booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx

Rob's Tangram Page, from: http://home.comcast.net/~stegmann/tangram.htm

Slocum Database, from: http://webapp1.dlib.indiana.edu/images/search.htm?scope=lilly/slocum

a.k.a.Richter Picco Nr. T1

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.125" x 2.125" x 3/8", 8 stone pieces, and problem sheet;

theAnchor Puzzle Bookdates this puzzle as first made in 1913;

puzzle tray slides into the right side of the box with a small tab to pull it out;

top and bottom of box edge says "Richter Rudolstadt";

same pieces in a smaller size asRichter 13 Tormentor;

problem sheet has 26 shapes, where problem 11 shows how to pack into the box)

The first of three miniature Richter puzzles referred to as Picco or Piccolo (Nr. T2 is the same asRichter 12 Pythagoras; and Nr. T3 is the same asRichter 8 Anchor Puzzle; with the parallelogram piece divided into two triangles); see theAnchor Puzzle Book.

Further Reading

Indiana Slocum Archive (photos of Picco versions ofNr. T1Nr. T2abc, Nr. T3ab) from:http://webapp1.dlib.indiana.edu/images/search.htm?scope=lilly/slocum

a.k.a.Richter Hamleys

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 2.125" x 2.125" x 3/8", 8 stone pieces, and problem sheet;

puzzle tray slides into the right side of the box with a small table to pull it out;

same pieces in a smaller size asRichter 13 Tormentor;

same size and pieces as Richter Piccolo Nr. T1, and like that puzzle,

problem sheet has the same 26 shapes, where problem 11 shows how to pack into the box)

Further Reading

Modern page of the London Hamleys toy store: from: http://www.hamleys.com/explore-stores.irs

"Schutzengraben-Geduldspeil"

"Zoologischer-Garten"

Richter Company, Germany, early 1900's.

(both puzzles cardboard box 3.1" x 3.1" x 1/2", 15 stone pieces, and problem sheet)

These two puzzles are the same except for the included direction sheet. TheAnchor Puzzle Bookdescribes the 1915 Trench Puzzle as made for World War I soldiers, and the 1916 Zoo Puzzle as a "neutral" puzzle made in Switzerland.

Richter Company, Germany, 1890's / early 1900's.

(cardboard box 3.75" x 3.75" x 1/2", 48 stone pieces, and booklet;

theAnchor Puzzle Bookdates this puzzle as first made in 1892;

described on pages 87-90, 122-124 of the 1893Hoffmann Book;

16 white right triangles, 8 white wedges, 8 black wedges, 16 black quadralaterals;

inside of the cover shows how to pack the pieces into the box;

inside of the box bottom has an add for "Dr. Richter's Pain-Expeller";

booklet has multi-language text inside covers and on pages A to Q at the front,

and 48 pages with 153 shapes to make)

LikeBlumenspiel(usingcurved pieces) andMeteor One(using marbles), more of a two-dimensional building set than a puzzle.

--- 307 --- Star Puzzle, Continued

Different box and booklet cover art from the puzzle of the preceding page,

but otherwise the same)

Richter Company, Germany, circa 1915.

(cardboard box 8.8" x 8.8" x 5/8", 52 colored stone pieces, 6.75" x 6.75",

with 12 page blue problem and green solution booklets of 36 patterns)

More of a two-dimensional building set than a puzzle. Described on page 86 of theAnchor Puzzle Book, this is one of a number of Richter "Mosiac" puzzles made in the World War I time period that used colored tiles. The tiles are colored differently on each side; below is shown the arrangement shown above flipped over (in the horizontal direction), and two sample pages from the problem and solution booklets:

F. Ad. Richter & Co., Germany, early 1900's.

(cardboard box 6.3 by 6.3 by 5/7 inches, 4 colors marbles, and booklet;

more of a game than a puzzle, the object is to arrange the marbles into patterns;

inRichter's Puzzles and Pastimescatalog - seeAnchor Puzzlereferences)

F. Ad. Richter & Co., Germany, early 1900's.

(wood box 8.75" x 8.75" x 2.5", 6 colors marbles, and booklet;

likeMeteor 1, arrange the marbles into patterns;

also includes aNine Mens Morris, board;

inRichter's Puzzles and Pastimescatalog - seeAnchor Puzzlereferences)

a.k.a.Richter Anchor Puzzle

Wood puzzle purchased circa 2000; sleeve made by J. A Storer.

(wood tray and pieces with cardboard sleeve, 5+78" square by 3/8" thick)

The sleeve has the problems from the classicRichter Anchor puzzle:

"Wm. F. Drueke & Sons, Grand Rapids, Mich.", circa 1940?

(cardboard box 2.5 by 5.75 by 13/16 inch thick, and 7 wood pieces;

assembles to a 4.1 inch square by 5/16 inches thick)

Tryne Games Mfg. Inc., Lindenhurst, NY, copyright 1961.

(cardboard box 5.6 by 9 by 7/8 inch thick, booklet, and 7 plastic pieces;

assembles to a 5.4 inch square by 3/16 inches thick;

the problems in the booklet are similar to theRichter 8 Anchor Puzzlebooklet; this puzzle should not be confused withRichter 12 Pythagoras)

(Same pieces asRichter No. 10 Cross Puzzle)

Kogner Bros. Inc., Tryne Game Division, East Paterson, N.J., circa 1960's.

(cardboard box 5.6" x 9" x 13/16" with plastic tray, booklet, and 7 plastic pieces;

assembles to a 5.4 inch square by 3/16 inches thick;

the problems in the booklet are similar to theRichter 10 Cross Puzzlebooklet;

the box and booklet are not dated,

but the booklet references a copyright 1961 version of theTangramthat it calls"Pythagoras")

(Same pieces asRichter No. 10 Cross Puzzle)

Hi Ho Puzzle, 1932.

(2.75 by 2.5 by 5/8 inch cardboard box, 7 plastic pieces, and directions)

The pieces are made fromBakelite(an old type of plastic developed in the early 1900's). Below are the top and bottom edges of the box and one of the sides (the other side is the same). The directions show a sitting dog and suggest that many other patterns can be made.

Further Reading

Wilipedia Bakelite Page, from: http://en.wikipedia.org/wiki/Bakelite

(Same pieces asRichter No. 10 Cross Puzzle)

Sherlock Holmes Puzzle, circa 1960.

(2.9" x 3.6" x 7/16" plastic box, 7 plastic pieces, and directions;

the next page shows another copy still glued to the original 8.2" x 6.25" card)

(Same pieces asRichter No. 3andRichter No. 16)

Scrambled Egg, Copyright ThinkFun 2002.

(9 metal pieces in plastic tray, 4 by 3.5 by 5/16 inches;

puzzle comes with clear plastic sleeve for storage;

booklet slides into tray bottom, and presents problems with solutions shown above)

Carrom Co., Ludington, Michigan, circa 1920s?

(cardboard box and 7 wood pieces, 3.6 inches square by 9/16 inches thick)

Like theAnchor Puzzle Tangram, the directions that were sold with this puzzle give a host of patterns to make from seven pieces similar to those of the Tangram.

ELZZUP Puzzle Co., Keene, N.H., circa 1900.

(3.3" x 3.3" x 3/4" wood box and 10 wood pieces)

This puzzle was sold in 2011 by a person who said it had been owned by Eleanor Dows of Laurel Mass., the sister of his grandfather, who was born in 1890. The back of the box top has her name in pencil, and her name and the town of Laurel Mass. is burned into the box bottom. The arrangment of the pieces into a square is not unique. In the spirit of theAnchor Puzzle Tangram, the goal is to make fun patterns with the pieces.

Wm. F. Drueke & Sons, Grand Rapids, MI, circa 1940's - 1960's.

(top: cardboard box 3.2"x3.2"x1/2", problem booklet, and 10 wood pieces;

middle: plastic box 8"x8"x1.2", problem & solution booklets, 10 wood pieces;

bottom: cardboard box 7.5"x7.5"x3/4", problem & solution booklets, 10 wood pieces)

In the same theme as theAnchor Puzzle Tangram, all three of these versions present 57 pages of 200 shapes to make. The first version above has only a problem booklet, which also includes English, French, and Spanish pages at the beginning that indicate that the puzzle may be purchased by mail for 50 cents, and that a solution booklet can be ordered for 25 cents; the back of this booklet shows how to pack the pieces into the box.

(from the 8x8" version)

(from the 8x8" version)

PIC-TUR-ETT Company, Mattapan, Massachusetts;

"PATENT APPLIED FOR"; all figures on directions and cards are copyright 1933.

(cardboard box, direction sheet, 15 problem ad solution cards, 4.25" x 4.25" x 1"))

Rockford Pattern Works, circa 1930's?

(4.25" square by 5/8" thick box, 9 wood pieces, and 4" square booklet;

some versions have theRinehimer Millwork labelon the box top)

Like theAnchor Puzzle Tangram, a booklet shows shapes to make. Here are thebooklet pages(page 1 and the last page are shown together):

Further Reading

King Tut Wikipedia Page, from: http://en.wikipedia.org/wiki/King_tut

Rockford Foundries History, from: www.rockfordfoundries.com/about.cfm

German text on the package promotes Vision 2000; purchased 2010.

(cardboard box and four 7/16" thick wood pieces, 9.25" x 1.8" by 9/16")

In the theme of theAnchor Puzzle Tangram, using the same four pieces as theMissing Tpuzzle, the booklet gives100 shapesto make, the first how to pack into the box and the last is the T:

Further Reading

Vision 2000 Page, from: http://www.vision2020.org/main.cfm

Copyright ThinkFun 2008.

(plastic, 5" x 5" x 1.4")

In the theme of theAnchor Puzzle Tangram, 14 pieces can be arranged into many shapes. The box has a tray that slides out with 60 problem cards of shapes to make (that give hints and solutions on the back).

Further Reading

Problem card backs.

Magic Square, circa 1960?

(plastic box 2.5 by 1.75 by 1/2 inches and 4 plastic pieces;

assembles to a 2.5 inch square)

a.k.a.Square Me, Five Block Puzzle, Madagascar Madness

ThinkFun Binary Arts, 2003.

(plastic, 4-piece square is 3 inches, solved 5-piece square is 3.2 inches square)

People often quickly find the four piece solution and then get stuck trying "stretch" the puzzle just a little bit in a way that will accommodate an additional small square piece. If the four piece solution is 4 units square, it has area 16, the extra square has area 2, and the five piece solution has area 18 (forming a square that is just under 4.25 units square); for each of the pieces in the four piece solution, its orientation is 45 degrees counter-clockwise in the five piece solution:

Characterized on page 102 of the 1942Filipiak bookFilipiak book as "recorded in the records of antiquity", has been periodically made as a promotional item.

CSPI promotional circa 1975.

(plastic, solved 5-piece 2.9 inches square;

this was a company that J. A. Storer's father was a part of in the 1970's;

came with a wire loop which J. A. Storer replaced in 2007 with Snowbird key ring)

"Madagascar Madness", Behavioral Sciences Inc., 1969.

(5 inches square by 3/4 inch thick plastic box and five plastic pieces;

the square piece was lost and replaced with a green plexi-glass piece)

This puzzle is packaged with a tray for the 4-piece solution and the 5th piece loose; perhaps to guide the solvers thinking away from the 5-piece solution. The directions on a 4.5 inch square card inserted into the back give an interesting discussion of the geometry:

Dickinson's Witch Hazel promotional, unknown age.

(3" x 4.5" envelope with cardboard pieces, solved 5-piece square is 4" square;

Dickinson's Witch Hazel was first made in 1866 and was still being made in 2000)

Five Block Puzzle, S.S. Adams Co. circa 1950?

(1/4 inch thick wood pieces, solved 5-piece square is 5 inches square)

http://www.lib.uconn.edu/online/research/speclib/ASC/findaids/

EEDickinson/MSS19960001.html

a.k.a.T Puzzle, Magic T, Cut-Up T, Pa's T Puzzle,

Great American T Puzzle,White Rose Ceylon Perfect T Puzzle,Lash Bitters T Puzzle.

Old design, copyright 1898 Lash Inc., this copyright ThinkFun Binary Arts 2003.

(plastic, 4 pieces, 3.1" high by 3" wide when solved)

The four pieces can be positioned to form a T as shown above. TheHIQUpuzzle has a booklet of problems based on these pieces. This is an old puzzle that has been produced many times; here is a nice antique wood one:

Pa's T Puzzle, circa 1940's.

(cardboard box 4.6 by 1.75 by 11/16 inches and 4 walnut pieces,

5" high by 4.75" wide when solved;

box edge says "PA'S T PUZZLE No. P 20 WM. F. DRUEKE & SONS Grand Rapide, Mich.")

S. S. Adams Co., circa 1950's.

(3.5" cardboard sleeve with cardboard directions and dark green plastic pieces)

Magic T Puzzle, unknown manufacture.

(plastic box 2.5 by 1.75 by 1/2 inches and 4 plastic pieces)

Marx Toys, circa 1960's.

(5.5 by 7 inch cardboard card with plastic pieces;

solution sheet in plastic bag and big question mark with company logo behind the bag)

Further Reading

T Puzzle Wikipedia Page, from: http://en.wikipedia.org/wiki/T_puzzle

"Shackman N.Y.1 No. 3627 Cross Puzzle", made in Japan, circa 1960's?

(cardboard box 5+1/8" x 1.75" x 5/8", direction sheet, and six 1/8" thick wood pieces

consisting of four identical Z shapes and two identical L shapes;

assembled cross is 4+3/8" high by 3 inches wide at the cross, and 1" wide at the tips.)

Hikimi Nob Yoshigahara Puzzle Collection, Japan, Copyright 1987.

(box and 6 wood pieces, 3.7" x 6.1" x 3/4";

included aredirectionsin Japanese that give the problems shown above)

Designed by T. Linden, made by E. Fuller, 2009.

(velour bag and 7 English Brown Oak pieces, 3 inches assembled)

There are two 1x1x3 unit pieces each with one 45 degree pointed tip, three 1x1x2 unit pieces each with one 45 degree pointed tip, and two unit triangles.

By cheating just a little bit, an upper caseHcan also be formed. On the left below the upper right tip of the H is missing a unit triangle. In the middle, the pieces have all been rotated 90 degrees and are arranged so that the H looks perfect from above (it is formed from two 3 unit pieces on the left, two triangles for the cross, and three 2 unit pieces on the right, where there is a missing triangle on the top right tip when viewed from the side). On right below, again the pieces have all been rotated 90 degrees and are arranged so that the H looks perfect from above (it is formed from a 2 and 3 unit piece on each side, a 2 unit piece and a triangle for the cross, and the remaining triangle filling in one of the tips, with the other three tips having a missing unit triangle when viewed from the side).

Promotional puzzle from Mr. Puzzle Australia, 2008.

(6 thin flexible plastic pieces)

Made by interlocking Puzzles 2000.

(directions card and 6 identical Zebrawood pieces, each 2.25 inches)

Here is what Interlocking Puzzles said:"There are at least eighteen different challenges requiring the special angles and three, four, five, or six pieces of our Make a Square puzzle. Geometric shapes possible include triangles, squares, rectangles, pentagons, hexagons, parallelograms, and trapezoids. This tiling puzzle seems simple, but it is quite challenging to find all the solutions. These 6 pieces are each over 2 inches long, which allows the largest finished shape to be over 7 inches across the diagonal."

Copyright B. L. Frye, St. Louis, MO, 1943.

(5 identical shaped large cardboard pieces and 5 identical shaped smaller cardboard pieces,

in a cardboard envelope 3+5/8" x 3+7/8", with directions on the inside)

Designed and mad by Stewart Coffin, 2013

(maple and paduk on a plywood bottom, 3.7 x 3.7 x 3/4", signed on the bottom;

one of 4 puzzles purchased during a visit with the designer in 2014)

Shown on page 155 of theCoffin AP-ART book. This puzzle is already a challenge due to the number of pieces and that they are two sided. Also, when it is given to someone with the pieces out of the box, there is a natural tendency to put them in so that they fit tight into the corners, in which case one inevitably ends up with having two pieces left that will not fit into the final corner. It is only after noticing that although the pieces are precisely cut, space is left between the packing and sides of the frame, and so something seems wrong (in fact, that space is equal to the space in the corners when the puzzle is correctly solved).

Designed by Stewart Coffin, made by Eric Fuller 2013.

(Ebony, Canarywood, Sapele, acrylic plastic top, 3.75" x 3.75" x 7/8";

6 puzzle pieces with the shapes shown above)

The plastic top has some rectilinear openings through which the pieces can be inserted and manipulated. Remove the pieces, mix them up, and then re-insert them. The underside has a rim that allows one to play with piece assembly without the plastic on top. Here is what the puzzle maker says:"I've constructed this with a solid Sapele body, shouldered on the corners for strength. The acrylic top is precision cut on the laser and the bottom is a solid floating canarywood panel chosen for contrast against the dark ebony. The fit is precise, with rounded corners to enable the very tricky rotational solution."The puzzle maker also quotes from the designer:"The three puzzles in this category all have a 5x5 square two-sided tray. On the back side is a simple framed square for practice exercises. The front side has a Plexiglas cover with openings cut in it through which the puzzle pieces are inserted. Of these three, The Decoy (#187-A) is by far the most difficult and my favorite. It is the only one that requires a slightly loose tray or rounding of corners to solve."

Plas-Trix Co., Jamica, NY, circa late 1950's

(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches)

Made by the same company and packaged like theKrazee Checkerboard Puzzleand theKrazee Links, but easier. Here are the packing instructions on the back of the directions and a solution:

Purchased 2004.

(wood base with metal pins, 7 wood pieces, 5 inches)

A board with metal pins must have 7 wood pieces (with holes) placed on it to form a square. The solution is not unique.

Copyright ThinkFun 2008.

(plastic, 3 inches)

Pack the four T's into the square. On the left above is the top side of the puzzle solved, and on the right above is the easier underside of the puzzle (with a larger square) solved.

Designed by E. Nagata, copyright Binary Arts 2002.

(plastic and metal, 3.5 by 4.5 by 3/8 inches thick)

The puzzle comes with the pencils placed on one side of the board as shown above. The challenge is to flip the board over and pack them into the other side:

Designed by Bill Cutler, made by Walt Hoppe, and purchased 2006.

(15 pieces including the pearl and shell, 4.5 inches)

The goal is to place the thirteen wedge shaped pieces and the pearl (the little round piece) into the shell. After achieving the configuration shown above, the pearl is off to the right in the keeper hole, the pieces meet at a point in the center, and there appears to be no extra space. Now for the fun; the pieces can all be flipped over and space made to place the pearl in the center of the shell:

Designed by Bill Cutler and made by Walt and Chris Hoppe, 2008.

(25 wood pieces, each 3/16 inch thick, solved puzzle is 6.5 inch diameter circle)

Pack the 25 pieces to form a circle; here is what the directions say:"These pieces can be used to tile the plane non-periodically. They are a variation of the Penrose "Kites and Darts" tiles. Each barn is equivalent to the Penrose "Dart" piece, and the silos and tractors are each one-half of a "Kite" piece."The graphics on the 25 pieces are:(5) barn with a silo

(5) barn with a double silo

(5) barn (no silo) with a tractor

(5) barn (no silo) with a tractor towing a cart

(3) barn with a double silo and tractor

(2) barn with a silo and tractor towing a cart

Note:The directions say that some puzzles were made with the quanties 3 and 2 reversed.Further Reading

Wikipedia Penrose Tiling Page, from: http://en.wikipedia.org/wiki/Penrose_tiling

Designed by Minoru Abe, purchased 2014.

(cardboard box, wood tray, and seven wood pieces)

Find all 7 ways to pack the 7 pieces, each consisting of 6 unit squares, into the tray that is 5 units high by 9 units wide with 3 units blocked out in the upper left corner; one is shown above, and here are the six others:

a.k.a.Polyominoes

Old puzzle, this one made by Yasumi, 1995.

(wood, box and 12 pieces based on 0.75" inch cubes)

The 12 distinct shapes formed from 5 connected squares are the pentominoes (called polyominoes by Solomon W. Golomb, Charles Scribner's Sons, NY, 1965):

Total area is 60, and sizes 6 x 10, 5 x 12, 4 x 15, and 3 x 20 can be formed. There are known to be 2,339 distinct ways to form a 6 x 10 rectangle, excluding rotations and reflections. In contrast, there are 1,010 solutions for 5x12, 368 solutions for 4x15, and 3 x 20 has a unique solution except for rotating a central portion by 180 degrees.

A piece is landlocked if it does not touch one of the borders of the rectangle. Eric Harshbarger has determined that there are no 6x10 rectangle solutions with 5 or more landlocked pieces, but there can be solutions with 0, 1, 2, 3, or 4 landlocked pieces (e.g., there are 207 solutions of the 6x10 rectangle with four landlocked pieces, 1,111 with three, 864 with 2, 155 with one, and only a couple with zero).

R. M. Robinson of the University of California at Berkeley proposed the "triplication problem": Given a pentomino, use 9 of the other pentominoes to construct a scale model, 3 times as wide and 3 times as high as the given piece (all 12 are possible).

Pentominoes are traditionally flat pieces that can be arranged to form 2-dimensional patterns. However, if the pieces are made to be 1-unit thick, then fun 3-dimensional patterns can also be made, including a 3 x 4 x 5 solid, and stairs that are 6 wide by 4 deep by 4 high.

(The shaded area of the 3x20 solution may be rotated by 180 degrees.)

From the directions sold with theYasumiversion:

From the directions sold with theInterlocking Puzzles version:

Made By B. Cutler, 1989.

(3.25"x4"x2.375" plastic box and 12 two-color wood pieces with 3/4" cubes)

Can be used like any other pentominoes set. In addition, it is made from light and dark woods so that it can be solved in a 3x4x5 box where colors have a checkerboard pattern on all sides. Here is the diagram of the pieces from the directions that came with the puzzle:

Sold with this puzzle was printout of a number of solutions. Here is the one suggested; the pieces have the names 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and this figure shows the three planes of the checkerbox:ABB5C A666C A636C

BB555 A7778 3333C

B9958 A9778 9944C

11111 22228 44428

From the directions sold with theYasumiversion:

Shown onNivasch's Page:

Further Reading

Harshbarger's Page, from: http://www.ericharshbarger.org/pentominoes

Mathworld Page, from: http://mathworld.wolfram.com/Pentomino.html

CIMT Page, from: http://www.cimt.plymouth.ac.uk/resources/puzzles/pentoes/pentoint.htm

Gerard's Page, from: http://www.xs4all.nl/~gp/pentomino.html

Huttlin's Page, from: http://members.aol.com/huttlin/pentominoes.html

Nivasch's Page, from: http://yucs.org/~gnivasch/pentomino

Mark's Page, from: http://mathsevangelist.wordpress.com/2012/08/24/packing-pentominoes

Jankok's Page, from: http://homepages.cwi.nl/~jankok/etc/Polyomino.html

info Page, from: http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html

Gottfriedville Page, from: http://www.gottfriedville.net/puzzles/colorgame/solutions.htm

Belgium Pentominoe page, from: http://home.scarlet.be/~demeod/indexe.html

Puzzle Will Be Played page, from: http://www.asahi-net.or.jp/~rh5k-isn/Puzzle

Fletcher's Page, from: http://www.andrews.edu/~calkins/math/pentos.htm

Wikipedia Page, from: http://en.wikipedia.org/wiki/Pentomino

Negahban Design Patent, from: www.uspto.gov - patent no. 385,311

Further reading about some related puzzles:

Lester Patent, from: www.uspto.gov - patent no. 1,290,761

Wadsworth Patent, from: www.uspto.gov - patent no. 3,964,749

Sarkar Patent, from: www.uspto.gov - patent no. 5,544,882

Designed by P. F. Ramos 2004, made by Interlocking Puzzles.

(wood frame and 12 pieces, 3.75" x 3.75" x 3" inches)

Standardpentominoesare the 12 different planar shapes that can be formed from 5 squares. There are 17non-planarpentomino shapes (each made from 5 cubes). Here, 12 of them (which can be can be grouped into 6 mirror image pairs) must be packed into a 4x5x5 box frame; 40 units are used by the frame, leaving exactly 60 units of space to pack these pieces:

According to the sheet that came with the puzzle there are 54,189 possible ways these pieces can fit (in the sense that you could build the box around them), of which 23,549 of them can be achieved by starting with the box frame and inserting and moving pieces. Here is the layer by layer representation of the solution that came with the puzzle (X is the box):

A

B

C

D

E

F

G

H

I

J

K

LIn the orientations shown in the figures above, pieces can be inserted as follows:

top layer:XXXXX

XJAFX

XJJFX

XCCFX

XXXXX2nd layer:XGAIX

GGAFF

GJAAK

HJCDK

XDDDX3rd layer:XGBIX

BBBII

EEELL

HHCKK

XDCKXbottom layer:XXXXX

XBEIX

XHELX

XHLLX

XXXXX

1. B from behind.

2. I from behind.

3. G from behind.

4. E from below.5. H from below.

6. A from behind.

7. L from the right.

8. K from the front.9. F from behind.

10. C from above.

11. J from the top.

12. D from the front.

a.k.a.Sneaky Squares, Stark Raving Cubes, Block Out, Square Fit, KUBI

Designed by Bill Cutler, wood version made by J. Devost, 1983.

(left: oak, 4.5 inches square by 2.25 inches high;

middle:Sneaky Squares / Start Raving Cubes, plastic, 4.5" square by 2" high;

right:Block Out / Square Fit, 3" square by 1.25" high)

Four pieces cut at odd angles (so that they not quite cubes) must be placed into the box (athree piece versionhas also been made). Inserting one at a time will not work. To solve, arrange them on the table so that the top is level and square, push them together at the bottoms, and drop them into the box. Here is what the pieces look like in their solved positions, outside the box:

a.k.a.The Third Degree

Designed by Bill Cutler, made by W. Hoppe, 1995.

(wood, 3.75 inches by 1.75 inches high)

Three pieces that are cut at odd angles (so that they not quite the same) must be placed into the box. Like the largerBlock Headpuzzle, putting them in one at a time will not work; to solve, first arrange them on the table so that the top surface is level and a hexagon, and then push them together at the bottoms and drop them into the box. Here is what the pieces look like in their solved positions, outside the box:

Designed and made by Stewart Coffin, 2014.

(maple pieces and sides on plywood base, signed on the bottom;

2.25" high, top edges of walls are 2", balls are 3/4" diameter;

one of 4 puzzles purchased during a visit with the designer in 2014)

Unpacking requires moving the top two pieces out of the way and removing the bottom one first:

Elverson Puzzle, 2002.

(wood box and 13 wood rods, 2.75 by 7.5 by 1.75 inches)

Pack 13 wood rods into the box. Here are th directions on the bottom of the box:

Here is the solved top layer taken out, showing the solved bottom layer in the box:

Made in the U.K., circa 2000?

(wood box and 18 wood rods, 2.7" square, with recessed silver dot stickers)

Pack the 18 rods into the box. A solution of 6 layers going from top to bottom is shown here from upper left to lower right (note that the rods of the top layer shown in the upper left all need to be rotated 180 degrees, as does the first rod in the second layer):

Copyright Pacific Game Company Inc., Japan, 1970.

(plastic, 3.25" square)

The object is to pull out all the pegs, mix them up, and reassemble. The instruction booklet shown on the following pages says there are 12 ways to do it, shows how to do two of them, and gives blank diagrams to color in the other ten solutions. Here is the solved cube shown above flipped over to show the other three sides:

Designed by John Conway, copyright ThinkFun Binary Arts 2003.

(plastic, box and 9 pieces, 1.75" solved)

Also known asConway's Curious Cube, and described on pages 736-737 of theWinning Ways books. Three unit cubes and six 1x2x2 pieces must be placed in a 3x3x3 box. In the unique solution, the three unit cubes line up diagionally through the cube from a corner to the center to the opposite corner:

Here is the solution that was sold with the puzzle:

"BRADLEY'S, CUBE ROOT BLOCKS, No. 2, TO TWO PLACES", circa 1940?

(wood box and 15 pieces, 3.25" square;

pieces based on 1/2 unit cubes;

two unit size cubes, one 3x3x3 cube, and three each of 1x1x3, 1x1x4, 1x3x3, 1x4x4)

Designer unknown, made by and computer analysis done by Bill Cutler 1979.

(wood box and 18 wood pieces, 4.8" by 6.8" by 1.7" thick)

A box of inside dimensions 18 x 28 x 6 units into which must be placed 18 two unit thick pieces of sizes 4x9, (2) 5x9, 5x18, 5x21, 6x7, 6x10, 6x13, (2) 7x8, (2) 7x13, 7x18, 8x18, 9x11, 9x13, 10x11, and 11x11. Cutler's analysis showed four solutions (not counting rotations and reflections), all placing the 4x9, 6x7, and 6x13 pieces on end. Here is one of them, from the sheets that came with the puzzle (copyright by and courtesy ofBill Cutler).

top layer middle layer bottom layer

Exchanging the middle and bottom layers gives a second solution, and these two solutions each have an alternate version by exchanging the 7x18, 5x21, 6x10 pieces on the top layer with the 7x13, 5x18, 10x11 pieces on the middle layer.

Designed by Bill Cutler with a computer 1992, made by Tom Lensch 2004.

(Wenge box with Bubinga pieces, 5 inches)

Here are the layers of the unique solution, from the sheet that was sold with the puzzle (copyright by and courtesy of Bill Cutler):

A host of puzzles have been made that require the solver to match adjacent edges or faces based on colors or patterns. Perhaps the most famous example of this type of puzzle isInstant Insanity, where one must line up four colored cubes so that each side has all four colors.

a.k.a.Rubik's Mini Tangle

Circa 1990, this one by J. A. Storer 2007 from a Rubik's Tangle 5x5.

(nine 2" cardboard squares in a 2.75 by 4 by 3/4 inch plastic box)

Arrange 9 squares in a 3x3 array so that edges match. Each square has the same pattern of 4 tangled ropes that has two connections on each edge. Different squares have a different combination of the four colors (red, green, blue, and yellow).

Jaap's Pageindicates that this puzzle may have been produced as a give-away to promote theRubik's Tangle 5x5puzzle. The puzzle pictured here was made by using squares from a Rubik's Tangle 5x5. It's solution is the upper left 3x3 portion of the first solution to Version 1:

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles

Thurston Patent, from: www.uspto.gov - patent no. 487,798

Rankin Patent, from: www.uspto.gov - patent no. 606,338

Produced in 1995.

(nine 2" square plastic pieces, patterns on both sides)

Arrange 9 squares in a 3x3 array so that edges match. Each square has on both sides the same pattern of 4 tangled ropes that has two connections on each edge. Different sides of different squares have a different combination of the four colors (red, green, blue, and yellow). More confusing thanRubik's Tangle 3x3because one has to decide how to flip the pieces.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/tangle.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/r90/tangle.htm

Thurston Patent, from: www.uspto.gov - patent no. 487,798

Rubik's Tangle 1, 2, 3, and 4, Matchbox 1990.

(Box and twenty seven 2 inch cardboard squares.)

Arrange 25 squares in a 5x5 array so that edges match. Each square has the same pattern of 4 tangled ropes that has two connections on each edge. There is one square for each of the 24 possible combinations of the 4 colors (red, green, blue, and yellow), and one duplicate square. The only difference between Rubik's Tangle 5x5Versions 1, 2, 3, and 4is which piece is duplicated. By taking three pieces from a spare set, a single set of 28 squares can be made where three of the duplicates are left out to make one of the 4 puzzles. Below is a set made by starting with a Version 3 and adding three squares taken from a Version 2; the four duplicate squares have been labeled with a number on the back.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/tangle.htm

Thurston Patent, from: www.uspto.gov - patent no. 487,798

Rankin Patent, from: www.uspto.gov - patent no. 606,338

"Made in West Germany" by Haba.

(3.75" x 3.75" x 1.8" cardboard box with nine wood pieces, each 1.75" x 1.75" x 7/16")

If the solution shown is rotated 135 degrees clockwise then it corresponds to the figure on the cover by mapping the four characters to the colors of the puzzle (in fact, by looking carefully, one can see a resemblance between the characters and the actual colored figures of the puzzle).

Price, Stern, Sloan Inc., Los Angeles, CA; Pig and Frog 1989, Train 1991.

(3.25 by 5.4 by 5/8 inch cardboard box and nine 3 inch cardboard pieces)

LikeRubik's Tangle 3x3, the directions on the back ask you to arrange the nine squares in a 3 by 3 array so that adjacent edges match; the Crazy Train directions state that there are exactly two solutions and are written in both English and Spanish.

Copyright 1997 McDonalds, GamesCo.

(cardboard box containing nine 5" square cardboard pieces)

McDonald Land Guzzle - "Birdie"

McDonald Land Guzzle - "Grimace"

McDonald Land Guzzle - "Bus"

a.k.a.Infants' Hospital - The Magic Line

Chad Valley Co. Ltd., Harborne, England, 1920;

made for the Infants Hospital in Vincent Square, London, founded by R. Mond.

(cardboard box and 16 cardboard pieces, 7" x 6.25" x 1/2";

instructions on the underside of the box top;

based on a 6x6 grid with four 1x3 pieces, and 12 1x2 pieces;

see alsoInfants' Hospital Puzzle,Dad's Puzzler - Exchange Version / Infants Hospital,A Ward In The Infants' Hospital,Infants' Hospital Jigsaw Puzzle)

The goal is to make the line go continuously from the start position at the bottom and end at the special "HEALTH" piece. Don't view at the solution before you try it; it's harder than it looks.

a.k.a.Endless Chain

Plas-Trix Co., Jamica, NY, circa 1957.

(plastic box and 14 plastic pieces, 4.75 by 4 by 5/16 inches;

same size / shape box as theKrazee Checkerboard Puzzlethat is shown

on pages 57-58 of theHaubrich book, which gives the manufacture date; a puzzle like this is shown as the "Endless Chain" on page 99 of the 1893 Hoffmann book)

Milton Bradley 1984.

(cardboard box and 12 plastic pieces, 7 by 5 by 1.5 inches;

"Lost Rope" is a translation of "Faden Verloren" that is written on the box.)

Made by Milton Bradley, 1987.

(plastic, 5 inches)

Remove the hexagonal pieces from the pegs and then try to put them back so that the numbers on all edges match. Same puzzle as theCircus Sevenpuzzle,, (numbers 1 through 6 correspond to the colors red, green, blue, yellow, white, and orange). For a computer, the solution space is small: 7 choices for the center piece, 6 choices for the first outside piece, 5 choices for the second, etc., for at most 7! = 5,040 positions to try. Here are the directions that came with it:

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm

a.k.a.Mind Exerciser

Masudaya, Japan, circa 1980's?

(4.25" by 1.75" high plastic box and seven hexagonal plastic pieces)

Arrange the seven hexagons so that adjacent edges match. Like theCircus Puzzler, but a larger size puzzle with different color patterns. This is the same puzzle asDrive Ya Nuts, (the colors red, green, blue, yellow, white, and orange correspond to the numbers 1 through 6).

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm

a.k.a.Color Matcher

Circa 1980's?

(2.9" by 1.5" high plastic box and seven hexagonal plastic pieces)

Arrange the seven hexagons so that adjacent edges match. Like theCircus Sevenpuzzle, but a smaller size puzzle with different color patterns.Jaap's Pageshows a number of other color variations for which this puzzle was made.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm

a.k.a.Spot Color

Made in China, purchased 2007.

(wood box and six wood circles with colored spots, 4 by 4 by 7/8 inches)

Arrange the six circles in a hexagon arrangement so that colored dots match; here is a closer view of the solution:

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm

Peter Pan Playthings, 1986.

(9.4 by 6.4 by 1 inch cardboard box, plastic base, and 6 plastic hexagons)

Jaap's Pagegives two solutions, the one shown above and this one::

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm

Unknown manufacturer.

(7 cardboard hexagons, 2.25" point to point, in a 2.75" x 4" x 3/4" plastic box)

Purchased from Mefferts, 2007.

(plastic bag and 9 cardboard triangles, each 4 inches on a side)

This puzzle comes in a number of patterns, this is the "Dizzy Dolphins" version:

Lagoon Games, 2000.

(2 by 6 inch cardboard box with 37 hexagonal cardboard pieces)

Instructions on the box:Solution provided by the manufacturer (http://www.give-me-a-clue.com):

Lagoon Games 2007.

(plastic box and 18 half hexagon plastic plates, 3 by 5 by 3/4 inches)

Form a big hexagon from the 18 half hexagon pieces so that edges match. Puzzles of some type using half hexagons have been around for a long time (e.g., the 1924 patent of A. Chrehore). Here is the solution provided by the manufacturer (http://www.give-me-a-clue.com):

Further reading:

Crehore Patent, from: www.uspto.gov - patent no. 1,495,576

a.k.a.Other Name

Patented by xxx, purchased from xxx.

(cardboard box and 8 cardboard pieces, 5.2 by 5.2 by 7/8 inches)

Copyright Binary Arts 1993.

(cardboard box and 15 cardboard pieces, 5.2 by 5.2 by 7/8 inches)

Copyright Great American Puzzle Factory, 1996.

(cardboard box and 17 cardboard pieces, 5.5 by 5.5 by 1 inch)

Patented by C. R. Weinreb 2000, made by Albatross Games / Toysmith Group 2006.

Transposer 6.

(6 cardboard pieces, each 3.5" on a side;

front and backs shown above)

Transposer Bonbons.

(6 cardboard pieces, each 3.5" on a side;

front and backs shown above)

Each circle on the plate is either colored or empty, and the problem is to stack the plates so that the two sides are a specified solid colors (Bonbons also gives some easier problems for one side).Jaap's Pagepresents solutions for these and some similar ones. Here are the problems given in the directions, which list them in order of increasing difficulty:

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/trixxy.htm

Weinreb U.S. Patent Application, from: www.uspto.gov - no. 2005/0225032

Same manufacture as Transposer 6 and Bonbons.

(4 cardboard pieces, each 3.5", backs shown below fronts in photos above)

Four plates must be stacked so that a path of a specified color on each side color connects the corner dots (and there are easier problems for only one side). Here are the ten problems that the directions list in increasing difficulty:

Tantrix Games 1997.

(holder and 10 plastic hexagonal pieces, 1.6 by 2.25 by 2.25 inches high)

Ten hexagonal tiles (numbered 1 through 10 on the backs) can be arranged in patterns, the highest level challenge being to make a loop of a given color (and matching edges of all adjacent tiles). The two sets shown above have different holders and background color, but the same tile patterns. Below, on the right are excerpts from the directions that came with the puzzles and on the left three ten tile loop solutions that are presented onJaap's Pagetogether with solutions to related puzzles (yellow and blue are switched from the sets shown here).

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/tantrix.htm

Tantrix Home Page, from: http://www.tantrix.com

Tantrix Games 1991.

(mesh bag and 10 plastic hexagonal pieces, 1.8 inches point to point)

LikeTantrix Discovery, ten hexagonal tiles (numbered 1 through 10 on the backs) can be arranged in patterns, the highest level challenge being to make a loop of a given color (and matching edges of all adjacent tiles) or to make a pyramid with a continuous line through it. Four colors are used (as compared to three with Tantrix Discovery). Here are solutions presented onJaap's Pagefor blue and red loops, a blue pyramid, and three red pyramids (the color white here is yellow there):

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/tantrix.htm

Tantrix Home Page, from: http://www.tantrix.com

Patented by K. Minami and T. Nishimiya 1984, made by Tomy.

(plastic with colored metal ball bearings, 4.3 inches square by 1/2 inch thick)

Turning a wheel on the side causes the center ring to turn one direction and all the other rings to turn in the opposite direction. When solved, the center ring and three of the outer rings have silver ball bearings, and the other three outer rings have bearings colored red, green, and blue, and the center ring is missing one ball bearing. The one missing bearing allows bearings to be moved around by turning the rings and transferring a bearing from one ring to an adjacent one that currently has the empty position. After mixing it up, it is difficult to get it back to the solved position because rings cannot be rotated individually.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/gears.htm

Minami and Nishimiya Patent, from: www.uspto.gov - patent no. 4,468,033

Copyright Eng's I.Q. Company Ltd. 1987.

(metal, 15 inches)

Each of 12 discs is colored with the same eight colors, but in different orders. The two discs on the left and right sides are attached to an arm (that rotates). In the center is a long arm, on its ends two shorter arms, and on their ends arms with pairs of discs. The discs themselves can all rotate. The task is to rotate the arms to place the discs in a straight line and then rotate the discs in such a way that colors match between adjacent discs and also between the left and right ends. The analysis onJaap's Pageshows that there are 12 ways to do this, but only one of them uses all eight colors:

Here is a side view of the arms when the discs are lined up in a straight line (as with a solved position):

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/spectra.htm

Lamphere's Article, from: http://portal.acm.org/portal.cfm

a.k.a.Katzenjammer, (Great) Tantalizer, Face-4, Cube-4,

Bognar Balls, Taktikolor, Frantic, Diabolical, Damblocks,

Symington's Puzzle

Patented by F. Schossow 1900, this popular version by Parker Brothers 1967.

(standard: four plastic cubes, each 1.25 inches square;

mini: four plastic cubes, each 5/8 inches square)

Arrange the cubes in a line so that each side has four different colors (it is not possible to arrange them so that all colors on a side are the same). The puzzle, in both the standard and the mini version, was sold without a box, wrapped with the directions:

The solution is unique up to the ordering of cubes or rotating them all 180 degrees in one dimension (the mini is the same except that green and red are reversed);

Further Reading

Wikipedia Page, from: http://www.wikipedia.org/wiki/Instant_Insanity

Rob Stegmann's Page, from: http://www.robspuzzlepage.com

Schossow Patent, from: www.uspto.gov - patent no. 646,463

Silkman Patent, from: www.uspto.gov - patent no. 2,024,541

Bognar UK Patent Application, GB 2,076,663.

Efficient algorithms are not known for finding Hamilton cycles (let alone two disjoint ones). However, this is a small graph, and it provides an organized way to search for these two cycles rather than playing with the cubes and trying to remember what has been tried.

- Draw four
vertices), and label themgreen,white,blue,red; it doesn't matter how they are arranged (after solving, the figure below was re-drawn to look nicer).- Number the cubes from 1 to 4 and for each of the three pairs of opposite faces on each cube, draw an
edgebetween the two vertices of the corresponding colors and label that edge by that cube number (a total of 12 edges).- Look for a
Hamilton cycle(that passes through each vertex once) with a different label on each edge; this cycle is shown with the thick edges below (it is also ok to use set of smaller disjoint cycles but that doesn't help here).- Find a second Hamilton cycle (or set of cycles) with a different label on each edge, that does not uses any of the edges in the first cycle; this cycle is shown with the hashed edges in the figure below.
- Traverse the thick edge cycle to set the top edges (green to blue set the top and bottom of cube 3, blue to white to set the top and bottom of cube 2, white to red to set the top and bottom of cube 4, and red to green to set the top and bottom of cube 1).
- Set the front/back edges with the hashed cycle by rotating each cube (without changing the top and bottom).

cycle 1:G - 3 - B - 2 - W - 4 - R - 1 - G

cycle 2:G - 2 - B - 1 - W - 3 - R - 4 - G

Parker Brothers, Copyright 1986, made in China.

(same size 1.25 inch plastic cubes as the 1967 puzzle)

Katzenjammer Puzzle, patented by Frederick A. Schossow 1900.

(cardboard tray & sleeve, and four 3/4 inch wood cubes)

Same as instant insanity with red -> hearts, green -> clubs, blue -> diamonds,

white -> spades, and cube 3 has the two hidden faces reversed:

These two puzzles have identical cubes (except the green color of the clubs on the right is faded). Here are the top, front, and back, of the two boxes, which are similar but not the same, and also the bottoms, where the one on the left is blank and the one on the right has promotional text:

FOURACE Puzzle, Britain, 1913.

(cardboard box 1+7/8" x 1+7/8" x 3+7/8", and four paper covered wood cubes,

where the cube edges vary in length from 13/16" to 15/16")

Box says "Provisionally Protected";Stegman's Pagecredits J. Slocum as dating this puzzle to Gamage's in Britain 1913. The solution is the same as for the Katzenjammer Puzzle:

Here are the top, front, back, and bottom sides of the box (the box back advertises "The Great Card Puzzle"):

Great Tantalizer Puzzle, provisional patent no. 18945, not dated.

(cardboard box, and four 3/4 inch wood cubes)

Same as instant insanity with green -> white, white -> brown, and cube 3 has the two hidden faces reversed:

Here are views of the left end, top, front, bottom, back, and right end:

Tantalizer, made in England, not dated.

(cardboard box, solution sheet, and four 3/4 inch wood cubes; packaged with tie wraps to cardboard back shown on right above)

Same as instant insanity with yellow instead of white:

The solution sheet that came with the puzzle shows the same solution as above,

with cubes in the order 1, 4, 2, 3 and all rotated 180 degrees:

Here are the directions on the bottom of the box:

Symington's Puzzle, W. Symington & Co., Harborough, England, not dated.

(cardboard tray & sleeve, and four 1 inch cardboard cubes)

Same as instant insanity with red -> IDEAL TABLE CREAM (red), green->SOUPS (light blue), blue -> CUSTARD POWDER (white), white -> GRAVY (red with brown triangle), and cube 3 has the two hidden faces reversed:

Here are views of the top, front, and back (the bottom is the same as the top):

"Face 4" made by Ideal Toy Co. 1980.

(tray, cover, and four 1" pieces,

same as Instant Insanity with red -> green and green -> orange)

"Cube-4", except for name on cover is identical to Face-4.

(tray, cover, and four 1" pieces,

same as Instant Insanity with red -> green and green -> orange)

Hungarian "Bognar Buvos Golyok", patented by Jozef Bogner 1981 (GB2076663).

(4 inches long, 1" diameter, balls rotate in place, white / brown / black balls,

same as Instant Insanity with the 1234 order changed to 3142

and with red -> yellow, green -> red/orange, blue -> green, white -> blue)

Taktikolor, manufactured in Hungary, circa 1980?

(box and four 1.5 inch square plastic pieces with colored paper stickers,

same as instant insanity with green->red, white->yellow, red->green,

and for both cubes 3 and 4 the hidden faces are reversed)

Frantic, Wellingtons Ltd Stamford, UK, 1982.

(box and four 1.5 inch square plastic pieces,

same as instant insanity with green->red, white->yellow, red->blue, blue->green

and with hidden faces of cubes 3 and 4 reversed)

Diabolical, Wellingtons Ltd, Stamford, UK, 1982.

(package and four 1.5 inch square plastic pieces,

same as instant insanity with green->1, white->2, red->3, blue->4,

and with hidden faces of cubes 3 and 4 reversed)

Cat Puzzle, Copyright 1996 K. Miller / Images & Editions Stamford Lincs, England.

(cardboard box 4.25" x 4.25" x 1.5", solution sheet, and four 1.375" plastic cubes)

The box back and solution sheet are shown below. The solution is the same as instant insanity with the hidden faces of cubes 3 and 4 reversed, where red = "WIDE EYED CAT", green = "TABLE CAT", white = "TARTAN CAT", blue = "WHITE CAT" (the columns of the solution sheet correspond to cubes 1, 3, 4, 2):

Crazy Cubes, circa 1960's?

(four 1.25 inch square wood pieces labeled with whisky and numbers;

same as instant insanity with green -> 1, white -> 2, red -> 3, blue -> 4)

Sold solved with plastic over the pieces in a tray, with the directions on the back of the tray and the solution sheet under the pieces, where the cubes are arranged as shown in these photos (left is top and front, right is bottom and back):

By exchanging the right two cubes and then spinning each cube 180 degrees, the same presentation as for instant insanity on the first page is obtained:

Damblocks, Schaper Manufacturing Co., Minneapolis, Minn., 1968.

(package and four 1.2 inch square plastic pieces with colored paper stickers,

same as instant insanity with white->yellow)

Made by RainTree and purchased 2000.

(box and 4 pieces, each 7/8" inches square,

same as Instant Insanity with red -> green, green -> yellow, white -> red)

Made by Mr. Puzzle Australia and purchased 2005.

(tray and 4 pieces, each 1.5 inches square,

same as Instant Insanity with red -> circle, green -> Square, blue -> hexagon, white -> diamond)

Circa late 1800's?

(7/8 by 7/8 by 2.1 inch box with three identical 5/8" wood cubes;

original label on top was lost and replaced by a copy from an identical puzzle)

TheGrand Army Of the Republicwas a veterans organization formed after the American civil war (see theWikipedia page). This puzzle has three identical cubes, each colored red, white, and blue on three pairs of adjacent faces. Like the four cubeInstant Insanitypuzzle, the object is to arrange the three cubes in a line so that each side has no duplicate colors. Below is a solution and its graph (constructed as for Instant Insanity); it is unique up to repositioning the puzzle and reordering the cubes (e.g., replacing cycle 2 by R - 3 - W - 1 - B - 2 - R is the same as rotating 180 degrees, rotating forward 90 degrees, and exchanging cubes 1 and 2):

cycle 1:R - 1 - W - 2 - B - 3 - R

cycle 2:R - 2 - W - 3 - B - 1 - R

Further Reading

Wikipedia Page, from: http://en.wikipedia.org/wiki/Grand_Army_of_the_Republic

a.k.a.The Allied Flags Puzzle

Valentine & Sons, Ltd., Dundee, British Manufacture, circa 1918.

(1 x 1 x 4.4 inch cardboard box and five paper covered 13/16" wood cubes;

labels from Henry's of Manchester are on side and bottom of box;

similar in name and theme to theAllies Flags Puzzle)

The cube sides have flags from World War I (British,French,Belgian,Japanese,Russian). Like the four blockInstant Insanitypuzzle, the object is to arrange the five cubes in a line so that each side has no duplicate flags. Here are the directions that came with it:

Here are two solutions and their corresponding graphs (constructed in the same way as for Instant Insanity), where in the first both cycles use the same Hamilton path, but in the second the first cycle follows a different route:

Circa 1920's?

(left / right bottom: 2.15" x 2.7" x 1" box and 5 paper covered 3/4" wood cubes;

right top: 1.3" x 4.2" x 1" box and and same cubes as puzzle on left)

Similar in name and theme to theAllies Flag Puzzle, cubes have flags from World War I (U.S.,British,Red Cross,Russian,Republic Of China). Like theInstant Insanitypuzzle, the object is to arrange the five cubes in a line so that each side has no duplicate flags. Here is a solution and its corresponding graph (constructed in the same way as for Instant Insanity):

cycle 1:US - 1 - Russian - 4 - British - 3 - Red Cross - 2 - Republic Of China - 5 - US

cycle 2:US - 2 - Russian - 3 - British - 4 - Red Cross - 4 - Republic Of China - 1 - US

Made in Japan, undated.

(Cardboard box 1.6" x 1.4" x 5.5" with 4 1+3/8" wood cubes.)

In the theme ofInstant Insanity, arrange the cubes in a row so that all four numbers appear on each side. Above is the solution and by numbering the cubes 1 to 4 going from left to right, the corresponding solution graph (unlike instant Insanity there are no colors, numbers are used to label both the cubes and the faces of the cubes).

Copyright 1976 Onsworld Limited, England.

(four plastic cubes, clues and solution cards, cardboard box 1+5/8" x 1+5/8" x 6.5")

In a theme a bit likeInstant Insanity, arrange the cubes so that all sides show an English word. Although the solution included has the letters in correct orientation on all sides, the directions do not say if it is allowed to have a letter on its side or upside down, and two of the letters, N/Z and U/C can be read differently depending on orientation. In the diagram above the letters on the outer and inside faces have their correct orientations, except the R and T on the right of the second and third cubes are rotated 90 degrees counterclockwise, and the D on the right of the fourth cube is flipped horizontally.

Here are the "clues" and solution cards provided:

Here are the top and bottom of the box:

Here are the front and back of the box:

Made in the Czech Republic 1983.

(box and six 1.2 inch plastic cubes)

Each of the six cubes has a different one of the colorsred,blue,green,yellow,white, andblackon each side. This puzzle is similar toDrives You Crazy, but with a different color pattern. Like the four blockInstant Insanitypuzzle, the object is to arrange the cubes in a line so that each side has no duplicate colors. Here is a solution and its corresponding graph (constructed the same way as for Instant Insanity):

cycle 1:Y - 1 - B - 2 - G - 3 - W - 4 - BK - 5 - R - 6 - Y

cycle 2:Y - 4 - G - 5 - B - 6 - W - 1 - R - 3 - BK - 2 - Y

Purchased from Mefferts 2007.

(six 1.5 inch foam cubes)

Each of the six cubes has a different one of the colorsred,blue,light blue,green,yellow, andorangeon each side. This puzzle is similar toIribako, but with a different color pattern. Like the four blockInstant Insanitypuzzle, the object is to arrange the cubes in a line so that each side has no duplicate colors. Here is a solution and its corresponding graph (constructed the same way as for Instant Insanity):

cycle 1:Y - 2 - G - 1 - O - 4 - LB - 6 - R - 3 - B - 5 - Y

cycle 2:Y - 3 - O - 6 - G - 5 - LB - 1 - B - 2 - R - 4 - Y

Based on a puzzle produced in 1899; this version made by J. A. Storer, 2011.

(plastic box 1.5" x 2.5" x 3.3", instruction card,

and four 1+3/16" painted wood blocks with vinyl stickers)

Arrange the cubes in a 2x2 array so that all four letters appear on the top and bottom faces, all four letters appear on the left and right sides, and all four letters appear on the front and back sides. The letters are based on the names of two Boer generals,Joubert andCronje, and two British generals,Buller andWarren, from an1899 productionof this puzzle.

We begin with a different puzzle; here the graph constructed as forInstant Insanity; we use letters to label faces and number the cubes 1 = green, 2 = red, 3 = brown, and 4 = yellow:

The two cycles, labeled by the thick edges and the hashed edges, give the following instant insanity like solution to arranging the cubes in a 1x4 array so that all for sides show the 4 letters; note that unlike the solution for instant insanity, one of the Hamilton cycles is actually a set of two cycles, a self loop and a cycle of three vertices:

cycle set 1:(J - 1 - W - 2 - C - 3 - B - 4 - J)

cycle set 2:(J - 2 - J) (C - 1 - B - 3 - W - 4 - C)

Solution idea:Unlike instant insanity, the graph of the preceding page does not give us a complete solution, because we cannot use disjoint cycle sets to simultaneously set both the top / bottom faces and the sides. Instead, we use each cycle set for a way to set the top / bottom faces that may lead to one or more complete solutions, by searching a new graph that describes the ways that cubes can be in a 2x2 array without changing the top / bottom faces. These secondary graphs are constructed below by going around the sides of each cube in a clockwise direction, where when we go from face X to face Y, we place a directed edge (an edge with an arrow) from vertex X to vertex Y (a total of 16 edges). We now look for cycle sets, but with the rule that the direction of arrows must reverse when going from one cube to an adjacent cube, or stay the same when skipping a corner (that uses a self-loop) and going to the opposite corner.

Solutions based on cycle set 1:Cubes 1 (green) and 4 (yellow) form self-loops; if they are adjacent then the red and green edges can be used to cycle between cubes 2 and 3, and if they are diagonally opposite, then the red and blue edges can be used to cycle between cubes 2 and 3. In both cases, and alternate solution can be formed by exchanging cubes 1 and 4:

Solutions based on cycle set 2:We find a solution based on self-loops for cubes 1 and 4 when they are diagonally opposite (and an alternate solution exchanges cubes 1 and 4):

Further Reading

Boer Wars Wikipedia Page, from: http://en.wikipedia.org/wiki/Boer_war

Patented by Jozef Bogner 1981.

(white / brown bodies, 1.7 inches)

Bolygok means planets in Hungarian. A generalization of the Hungarian version of Instant Insanity ("Bognar Buvos Golyok"). Rotate the balls to make patterns such as each side with all four colors or each side with the same color. The directions that come with it are in a long strip; here are pieces of it:

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/bolygok.htm

Bognar UK Patent Application, GB 2,076,663.

KMS Industries, Alexandria, VA, 1968.

(plastic, 1.75 inches;

directions are in the bottom)

Take the eight cubes out of the case and arrange them in a single 2x2x2 cube to make different patterns. The cubes have one of the colorsred,blue,green, andwhiteon each face. The card that is in the bottom of the cage challenges give a number of challenges, including making each face showing all four colors:

KMS Industries, Alexandria, VA, 1968.

(plastic, 1.75 inches;

directions are in the bottom)

Each of the eight cubes has three colored rods going through it, one in each of the x, y, and z directions (four of the cubes have ared,blue, andwhite rod, two of the cubes have two reds and a white, one has two reds and a blue, and one has two whites and a blue). Take the eight cubes out of the case and arrange them in a single 2x2x2 cube to make continuous rods of the same color passing through it:

Handle says "Clementoni"; unknown date of manufacture.

(plastic with paper surfaces, 12 pieces, 6 by 6.5 by 1.75 inches)

Position the blocks to make a Disney scene. Newer puzzles of this type are shown on the 2008 Clementoni web page (www.clementoni.com) as their 12 piece "super color cubes".

a.k.a.Spots Puzzle

St. Pierre & Patterson Mfg. Co. 1957.

(cardboard tray and nine 2 x 5/8 inch wood bars with recessed white dots;

shown as the "Spots Puzzle" on pages 98-99, 130-131 of the 1893Hoffmann book)

Assemble nine 1x1x3 unit bars into a die; from left to right in the photo above, the dots are:Here are close-up views of portions of the back of the box:

1. no dots

2. left end

3. top center

4. top center

5. top left, end right6. top left & right

7. top left & right, end left & right

8. top left & right, end left & right, front right

9. top left & right, end left, front left & right

Pentangle Puzzles And Games, England, 2009.

(plastic box and 9 L-shaped wood pieces, 1+7/8 inches)

Assemble the nine L-shaped pieces into a die, with either legal green spots on the outside or legal red spots. Sold in the green solution, which is a "right-handed" die; the red solution is a "left-handed die". Directions tell how to get a "Certificate of Failure". Here are photos of two stages of taking these two solutions apart:

Copyright Warner Brothers 1992.

(wood base and 8 blocks, 4 inches)

Slide the 8 blocks onto the 4 posts to make a 2x2 cube so that each of the 4 sides shows a single character. Below are photos of the other two solved sides and the blocks arranged to show the 8 distinct characters used (each block has some combination of 4 of these):Tweety Bird,Bugs Bunny,Road Runner,Daffy Duck,Marvin the Martian,Sylvester,Wile E. Coyote,Taz(Tasmanian Devil).

Copyright 2003 & Design Patent 2006 by Use Your Head Unlimited.

(plastic, base + top + 10 pairs of 1" diameter balls)

There are 10 pairs of colored balls, one pair for each of the possible pairs of the five colors white, yellow, orange, pink, and blue:

These pairs must be placed to form a pyramid so that no two balls of the same color are touching. The directions say that you should also not allow the same colors to touch as you are building, even for places that are not visible when the puzzle is completed. This is a relatively easy puzzle that is fun for children. It has more than one solution. The puzzle pictured here is the golf version; the same puzzle has also been advertised / sold with other sports themes (soccer, baseball, basketball, tennis, football).

The manufacturer has filed a number of design patents relating to this puzzle and its junior version. P. Roberts and A. Kuwagaki & S. Takenaka have 1970's patents on pyramids using pieces formed from more complicated arrangements of balls.

Further reading:

Thompson Design Patent, from: www.uspto.gov - patent no. D524,381

Roberts Patent, from: www.uspto.gov - patent no. 3,945,645

Kuwagaki Patent, from: www.uspto.gov - patent no. 3,837,652

Copyright 2000 & Design Patents 2005 by Use Your Head Unlimited.

(plastic, base + top + 5 pairs of 1" diameter balls

There are 5 pairs of colored balls, using the colors white, yellow, pink, and blue (all of the 6 possible combinations except pink-blue):

These pairs must be placed to form a pyramid so that no two balls of the same color are touching. The directions say that you should also not allow the same colors to touch as you are building, even for places that are not visible when the puzzle is completed. This is a relatively easy puzzle that is fun for children; it has fewer pieces that theSmarts Puzzle4 high pyramid made by the same company. It has more than one solution. The puzzle pictured here is the golf version; the same puzzle has also been advertised / sold with other sports themes (soccer, baseball, basketball, tennis, football).

Further reading:

Thompson Design Patents, from: www.uspto.gov - patent nos. D500,533, D500,534, D500,535, D500,816.

Probably made in Hungary in the 1980's.

(plastic, 3.5 inches)

Made by Tantrix, purchased 2007.

(3 inches)

Rotate the hexagonal and square faces so that the edges match. Fairly easy to solve because by starting at one vertex where three faces meet, there are not many possibilities, and then you can start working your way around. The bottom face of the Hungarian version is plain black. The faces of the tantrix version ("The Rock") can also be snapped off and put on in different positions to make different puzzles.

The 1983 patent of Sasso describes a similar idea for a regular solid shape where pairs of opposite faces rotate together.

Further Reading

Sasso Patent, from: www.uspto.gov - patent no. 4,416,453

Patented by REFO Verlag GmbH 2002.

(plastic, 2.6 inches)

Turn the 6 rings so at each of the 12 places they meet the colors match. This is a slightly simpler and more colorful version of theTurn 12puzzle that as 24 numbers on each ring (each in the range 3 to 9, where matching is by adjacent numbers summing to 12 - seeJaap's Page). Here are the directions that came with the puzzle:

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/turn12.htm

REFO DE Patent, from: www.epo.org - patent no. DE20112728

Patented by Rubik 1991, copyright Matchbox 1990.

(3.5 inches)

When assembled, the four sides of the pyramid are red, blue, yellow, and white. Moves consists of unsnapping a portion rotating it and snapping it back on.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/triamid.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/r90/trmd0.htm

Rubik HU Patent. from: www.epo.org - patent no. HU207233

Although cubes and various types of burrs are among the most common shapes for assembly puzzles, beautiful craftsmanship, often from wood, has gone into puzzles of many shapes. Some employcoordinate motion(a term used byStewart Coffin) where pieces must be slide together simultaneously when assembling.

Patented E. Johnson 1940, David Co. circa 1990's?, lower right circa 1960's?.

(top: 3.5"x2.7"x1.4" box, two 3" wood pieces, and directions;

lower right: 2.5"x1.75"x1/2" plastic box and two plastic pieces)

Further Reading

Johnson Patent, from: www.uspto.gov - patent no. 2,216,915

Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.

(Jarrah, 3 pieces, each edge 3.5 inches when assembled)

Box says "MADE IN U.S.A. S.K. & CO.", circa 1950?

(cardboard box and 4 wood pieces, 2.5 inches)

Like the classicTwo Piece Pyramidwhere each piece has been cut in half. Here are photos of it being assembled:

Designed by W. Schneider, copyright Binary Arts, 1998.

(4 identical plastic pieces, 3.25 inches on a side when assembled)

Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.

(Jarrah and Maple, 4 pieces, each edge 4.75 inches when assembled;

as shown above, comes apart into two 2-piece assemblies)

Designed by Wayne Daniel, made and sold by Interlocking Puzzles, 2003.

(Paduk and Maple, 4 pieces, 3.5 inches)

Two pairs of identical pieces slide together simultaneously. The solved puzzle has a maple diamond on each face where one point meets the point of a diamond on an edge shared with an adjacent face. Here are views of the start of coming apart, and the four pieces:

To solve, as shown on the left below, determine how to assemble two halves that are in the solved state, spread each apart to just coming apart, and with one par in each hand position carefully so that everything can be pushed together. The photo on the right below shows the side not shown in the photo at the top of this page.

Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.

(Jatoba and Maple, 5 pieces, each edge 6 inches when assembled;

as shown above, comes apart into a 3-piece and 2-piece assembly)

Designed by Steve Smith, made and sold by Interlocking Puzzles 2004.

(sequential assembly version: Maple, 4 pieces, 3.5 inches,

simultaneous movement version: Jarrah, 4 pieces, 3.5 inches)

These two puzzles have the same size and shape, with six square faces and eight hexagon faces; they were both designed bySteve SmithofInterlocking Puzzles(Interlocking Puzzles also made a third easer puzzle of the same size and shape that was designed by Wayne Daniel). The one on the left above requires sequential assembly of the four pieces in a specific order. The one on the right requires all four pieces to move simultaneously. Here is some of what the designer said about this simultaneous movement and a photo of the puzzle coming apart:"All four pieces must move simultaneously; there are two pairs of mirror image pieces made from Jarrah. There are 4 "solid" faces where the entire face is part of the same piece and four "multi' faces where the face has sections from three different pieces. Two of the multi faces (which are opposite each other) have a triangular shaped section, a diamond shaped section, and a trapezoid shaped section (the other two have two triangular sections and one larger non-convex section); by holding on to these two faces you can push the puzzle apart (all eight faces remain parallel as the puzzle expands)."

a.k.a.Cuboctahedron

Designed by Steve and Leslie Smith, made and sold by Interlocking Puzzles 2004;

box made by J. A. Storer 2004.

(5 pieces: Jatoba, 4.5 inches,

6 pieces: Peroba Rosa, 4.5 inches,

7 pieces: Jarrah, 4.5 inches,

box is 3/8 inch plexiglass with metal hardware, 5 by 5 by 12 inches)

These three puzzles have the same size and shape, with six square faces and eight triangular faces (corresponding to where the corners of the cube have been truncated). The five piece version was designed by Steve Smith and the 6 and 7 piece versions by Steve and Leslie Smith. Here is some of what they say about these three puzzles:Five piece Truncated Cube:"Each piece is a challenge, even after removing the first three, getting the last two apart and together isn't easy. Reassembly? Let's just say this should NOT be the first polyhedra puzzle of ours you work with."

Six piece Truncated Cube:"A small internal space requires multiple moves to get the first piece out."

Seven piece Truncated Cube:"Unique trilateral symmetry makes this puzzle quite difficult. This puzzle can be thought of as two three piece puzzles, with a key piece that holds it all together."

Designed by Stewart Coffin, purchased from Cubic Dissection 2004.

(wood, 6 pieces, 2.5 inches)

Purchased from Toys From Times Past, 2014.

(3 identical pieces, each made from 4 3/8" thick parallelograms;

when assembled 3" side to side, 1.5" high)

A first the pieces seem locked together. The pieces move simultaneously to disassemble, and the trick is to push on the top layer in the correct way to spread them apart:

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.

(mahogany, 3 pieces, 4 inches;

one of 6 puzzles purchased during a visit with the designer in the early 1980's)

Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"The one symmetrical face of the assembled puzzle happens to resemble a certain corporate logo. The company wanted a simple puzzle incorporating this pattern for some sort of promotional scheme. So the arrangement of six of the blocks was already determined. All that was required to complete the design was the addition of four more blocks in a sort of triangular pyramid and a judicious choice of glue joints to make it into an interesting interlocking puzzle. So the company got what they wanted - except for one thing. It turned out to be anything but simple!"When apart, it is hard to visualize what it is supposed to look like when assembled (although once assembled, you know you have it). Here are photos showing the piece orientations for assembly and the first of the two steps that puts together the two three block pieces:

Vin & Co., purchased from Bits & Pieces 2007.

(wood, 6 pieces, 3.5 inches)

Here are the directions and solution that were sold with the puzzle:

Designed and made by Stewart Coffin, 1997.

(wood, 3.25" by 1.75" high, each pod is 1.5" between parallel faces;

written to the right of the International Puzzle Party sticker

is the designer number / signature / date)

Three pieces come apart with simultaneous movement:

Designed and made by Stewart Coffin, 2010.

(wood, 3.25" by 1.75" high, each pod is 1.5" between parallel faces;

signed on the inside;

one of 4 puzzles purchased during a visit with the designer in 2014)

The name of this puzzle appears to come from theThree Bunnies puzzle, which has the same size and shape and is 118 in the author's new numbering system in theCoffin AP-ART book.

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.

(left: Mahogany, 6 pieces, 4 inches

right: Cherry, 6 pieces, 4 inches;

the one on the left was purchased at auction in 2001, the cherry one on the right is

one of 6 puzzles purchased during a visit with the designer in the early 1980's;

he called this cherry one a "crude loose-fitting prototype",

but of course it has terrific fit, and although it has some nicks

and pencil marks on the interior edges, overall it is a beautiful puzzle)

Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"To disassemble, grasp the opposite pairs of pieces, and gently pull and wiggle until you discover the combination that separates it diagonally into halves. The wiggle the pieces apart until you discover the strange action that separates each half into three pieces."The name is a joke that implies that each of the three axes is formed from some sort of pair configuration; that is, the implication being that the puzzle works something like a burr, where pieces slide in and out parallel to the three axes. In fact, it splits into two halves of 3 pieces each along a diagonal plane. Then, the two halves each come apart by simultaneous motion of all three pieces. Below, the left shows the two halves and the right shows one of the pairs:

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.

(Cherry and Rosewood, 6 pieces, 4.5 inches;

one of 6 puzzles purchased during a visit with the designer in the early 1980's)

Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"The Augmented Four Corners Puzzle consists of six dissimilar interlocking pieces which assemble in one way only, with one sliding axis, to form a geometrical solid with tetrahedral symmetry."Use the three pieces shown below to put together the top (shown with a rubber band) so that the "legs" that hang down have vertical sides that will slide down onto the other three pieces.

Design Science Toys LTD, Tivoli, NY, circa 1990's?

(wood with magnets, 4 inches)

Wood pieces with magnets, each in the shape of a rhombic hexahedron (a slanted cube), can be assembled into shapes, including the same shape as theAugmented Four Cornerspuzzle. The sheet that comes with the puzzle motivates the use of these pieces from the angles found in carbon molecules.

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.

(Rosewood and Tulipwood, 6 pieces, 4 inches;

one of 6 puzzles purchased during a visit with the designer in the early 1980's)

Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"This puzzle has the most unusual capability of being assembled into three different symmetrical solid shapes, even though its six pieces are all identical in shape."Four assembled shapes are shown in Stewart Coffin's bookGeometric Puzzle Design; where he discusses the 4-pieceFusion Confusion; version of this puzzle. One shape is the "star" shown above (6 points running vertically); below are two ways to pull it apart into two sets of three pieces. Another is the "hex ring" (a vertical hexagonal cylinder with a ring around the middle) that is show below, and to its right a way to pull it apart. Note that rubber bands have been used in these figures to hold pieces in place while photographed.

Designed by Stewart Coffin, made by interlocking puzzles 2001.

(Paduak and Guatam, 4 pieces, 3.3 inches)

The four pieces of this puzzle are formed by joining two pairs of the six pieces of theTriumphpuzzle. Triumph is described in Coffin's bookThe Puzzling World of Polyhedral Dissections, and this puzzle is described in his bookGeometric Puzzle Design, where he says that it has all of the original four solutions of the original Triumph puzzle, but with "only one confusing diagonal axis of assembly". To make the star shape, first join two pairs, and then slide the two halves together:

Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.

(Mahogany, 6 pieces, 4 inches;

one of 6 puzzles purchased during a visit with the designer in the early 1980's;

handwritten on the directions Stewart Coffin says "second, nicks and scratches, poor fit";

of course, as you would expect, the puzzle looks great and has a good fit)

Described in Stewart Coffin's bookThe Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"Examine the six individual puzzle pieces and note that there are three identical pieces which we shall arbitrarily refer to as "left-handed" pieces, and three right-handed pieces likewise identical except that one of them has a tapered hole with a pin stuck into it. To assemble thepinwheelsolution, first remove the pin and set it aside. Sub-assemble the three left-handed pieces into one sub-assembly, and the three right-handed pieces into another, and mate the two halves. The resulting solution has an axis of symmetry. The other symmetrical solution, known as theRosebudsolution, requires the simultaneous manipulation of all six pieces."

Designed by Stewart Coffin, made by interlocking puzzles 2002.

(Peroba Rosa, 12 pieces, 5 inches)

InGeometric Puzzle Design, Stewart Coffin says: "Twelve sticks of triangular cross-section with pyramidal end blocks assemble with some difficulty to form a symmetrical interlocking burr." Here is the solution that was sold with the puzzle (pieces are numbered in assembly order):

Assemble pieces #1, #2, and #3 to form a triangular base.Step 1:

When in place piece #4 will stand vertically with piece #5 parallel to piece #3. Piece #5 is the only piece with an extra augmentation. Assemble with the augmentation directly to the left of piece #2. Hold #4 loosely to allow #5 to slide in under the hook of #2.Step 2:

When in place piece #6 will be parallel to #4. To assemble, piece #6 hooks around #2 from below and slides up through next to #4.Step 3:

When in place piece #7 will be parallel to piece #1. To assemble, first push piece #1 all the way into the puzzle. This allows piece #3 to move to the left giving room for piece #7.Step 4:

Insert piece #7. Slide piece #3 back to the right and #1 forward.Step 5:

When in place piece #8 will be parallel to piece #2. To assemble, place #8 on the right side by hooking around #4 and sliding through #1.Step 6:

Now the puzzle has enough pieces in place to hold together better. When in place piece #9 will stand vertically, parallel to piece #4 and #6. To assemble, drop #4 down and move piece #7 back away from you. Bring #8 towards you until enough opening is made to allow for #9.Step 7:

Insert #9 by hooking around #3. Push #8 back in place to allow #4 to come back up. Make sure #9 is all the way down to allow #7 to slide back towards you. Bring #9 up to its final place. When in place piece #10 is parallel to #5 and #3. To assemble, hook the end of #10 around #8 and slide left under #9.Step 8:

When in place piece #11 is parallel to #8 and #2. To assemble, first drop #4 and #6 down. Slide #8 all the way towards you. Then move #10 to the left just enough.Step 9:

This allows #11 to be inserted underneath #10 with its end hooking around #7. Slide #10 back to the right. Now #8 slides back to allow #4 up. Make sure #11 is all the way towards you to allow #6 to come back up.Step 10:

Move #11 to its final place. Then the key piece #12 moves in parallel to #7 to touch the augmented place on #5.Steps 11 & 12:

"Crystall Pyramide", made in China, purchased 2009.

(15 wood pieces and base, 5.75 by 5.75 by 3.5 inches high)

Pieces formed from wood rods glued together must be placed on a base (that has some black rods glued to it) to form a pyramid; here is the solution that was sold with the puzzle:

Received as a gift from D. Storer, 2005.

(Cherry, 12.5 inches assembled)

Pull out the white peg that goes through to make the eyes, and the puzzle comes apart in a mor or less linear fashion; about midway through there is a small compartment containing a wood duck:

B. B. Shackman & Co., New York, circa 1940?

(wood, 1.7 by 1.7 by 2.9 inches; end not shown says "MADE IN U.S.A.)

Unknown maker, circa 1930's?

(wood, 3/4 inches square by 3 inches long)

A simpler 3x3 version (3 wavy horizontal cuts and 3 wavy vertical cuts) of the 4x4 puzzle described on page 109 of the 1893Hoffmann book.

From the grandfather of J. A. Storer; circa 1900?

(wood, 2.4 by 2.75 by 1.9 inches)

A simpler 3x4 version (3 wavy horizontal cuts and 4 wavy vertical cuts) of the 4x4 puzzle described on page 109 of the 1893Hoffmann book.

Patented K. Walker & designed with H. Nelson, made by Binary Arts, circa 2000.

(four plastic pieces, 4 x 4 x 3/4 inches assembled)

The four pieces do not simply come apart as it appears they might; careful positioning and twisting is required; here is the solution that was sold with the puzzle:

Further Reading

Walker Patent, from: www.uspto.gov - patent no. 5,409,227

Made in Japan, circa 1960's?

(wood, 1+7/8 inches)

Designed by Oskar van Deventer, made by Eric Fuller 2010.

(Pau Ferro and Quilted Maple, 3 inches)

Five pieces, each composed of the shape of a matchbox cover attached to a matchbox tray assemble to a single shape. Here are the pieces:

The two pieces on the top left slide together, then as shown below the pairs of vertical pieces slide together (and the third step slides the two halves together):

Purchased from Puzzles and Brain teasers EBay Store 2007.

(wood dowel and 6 wood pieces with dowels, 2.75 inches;

shown on Page 70 ofCoffin's Bookon Polyhedral Dissections)

Six wood pieces with pegs and a key peg (the key peg has a little pin to make friction so it does not fall out of the solved puzzle). Here are solution steps:

Purchased 2006.

(Walnut and Oak, 8 pieces, 5 inches by 3/4 inches thick)

Assemble three pairs and then push together simultaneously:

Purchased from Mr. Puzzle Australia 2006.

(wood, 11/16" cubes, 2.75" x 3.5" x 2" when assembled)

This puzzle is constructed likeKev's Cubes. Here, 31 wood pieces (30 unit sized cubes and one 1x1x2 piece) are connected by an elastic cord, and must be manipulated into the shape shown in the photo above.

Circa 1980's.

(plastic, 4 inches as assembled above)

A sequence of linked plastic pieces that can an be folded into fun shapes. The "solved" position is a 3D diamond shape shown above that fits into the plastic ball in which the puzzle was sold.

Further Reading

Rubik's Snake Booklet, from: http://www.rubiks.com/World/~/media/Files/hint_snake.ashx

McFArren's Page, from: http://www.geocities.com/abcmcfarren/math/snake2d.htm

McFarren's 3D Page, from: http://www.geocities.com/abcmcfarren/math/snake3d.htm

Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik's_Snake

Sold by Bits and Pieces 2007.

(aluminum, 4 pieces, 2.5 inches)

Four aluminum pieces fit together; here are four basic solution steps:

Identify the two pairs:Step 1:

Put the left pair together:Step 2:

Add the third piece:Step 3:

Slip on the fourth piece:Step 4:

a.k.a.Cigar Puzzle

Garner Products, New York; this one for sale in 1950's.

(wood pieces on metal spindle, 5.2" long x 3/4" diameter)

This puzzle was purchased from a seller who said that it came from residual stock ofGlenn's Novelty Shop, 16th and Market St., Philadelphia, where his father worked when the shop closed shop in 1959. Subsequently I received an email from Michel van Ipenburg, a puzzle collector, who kindly shared the image of the directions to this puzzle that are shown on the following page. The directions list objects to make from the pieces, including:

Chinese

Lantern

Knife

Grinder

HotWater

Bottle

Fire

Siren

Hitching

Post

Urn On

Pedestal

Circa 1960's.

(plastic, 2.75")

These keychains, barely a puzzle, became popular in the 1960's and have been made over the years for numerous objects, animals, shapes, etc. over the years. Here are three more examples and the directions that came with them:

(1.75" high)

(1.8" long)

(1.75" high)

Circa 1950's.

(plastic, 3.25" high by 2.25" diameter)

Fabricated on a 3D printer by L. Milekic 2016,

from a 3D print design by G. Frost,

posted in 2012 on the web page http://www.thingiverse.com/thing:26334.

(PLA plastic, 2" x 2" x 1.5" thick)

The two white pieces are the same shape but are not quite the same dimensions. Similarly, for the two dark pieces (that are symmetric to the white pieces). So first match each white with its corresponding dark piece. The two white pieces slide together on one plane and the two dark pieces slide together on a perpendicular plane. Start by putting three together and see how the fourth fits in. Then spread them all apart just right with the fourth piece now in position, and push together with simultaneous movement. Takes a bit of dexterity.

The great thing about the classicRubik's Cubeis that you don't have a bag of pieces when it is unsolved. Keep it on a coffee table, pick it up, play with it, and put it down when get tired. The original 3x3x3 Rubik's cube started an entire class of manipulation puzzles.

First patented by Rubik 1983, other patents cover different internal mechanisms.

(plastic, 1.5 inches)

Rubik 2x2x2 Three Step Solution

L (left), R (right), F (front), B (back), U (up), and D (down) for 90 degree clockwise rotations of that face, - means counterclockwise. Corners are named with three letters.Notation:

1.Solve the down layer.

2.Put the up layer corners in correct locations (but possibly rotated incorrectly):Use the following sequence exchange two corners:

FLU <-> FRU:( F U ) (F- U-) (L- U- L)

A quick way to do UBL <-> UFR is to precede this byNote:Land skip the finalL.3.Fix the up layer so all corners are rotated correctly:Position the cube so the up front right corner is not correct and repeat these two steps until all up corners are correct:

- Repeat until the up front right corner is correct:

(R- D-) (R D)

- Rotate the up layer so the up front right corner is not correct.

Note:During Step 3, the down layer will be mixed up, but it will become correct again at the end. Be sure to do all four moves of Step 3A each time; it is easy to forget the finalDwhen you see the correct color on top.

Notes About The Rubik 2x2x2 Three Step Solution

Get three corners right, move two of the correct ones 90 degrees, move the fourth into position, and move the two correct ones back. If the 4th corner is rotated so it won't position correctly, do a full 180 degree turn of that side and then you can reposition it to try again. In any case, even if this description is hard to follow, after playing a bit, this step becomes easy.Step 1:

This step could be replaced by:Step 2 - an easier but slower solution:If possible, rotate the up layer to be correct, except some corners may by be rotated; otherwise, mix up and go back to Step 1 using a different color on the bottom.Step 2.

(Starting from a random position, there is a 1 in 6 chance that this test succeeds. So even if a quick mix and starting with a different bottom is not completely random, once you get reasonably fast at doing Step 1, it shouldn't take too long.)This step can be used three times for a diagonal exchange. However, since it does not change the upper back left corner, it is faster to do UBL <-> UFR by preceding the transformation withStep 2 - making it faster:Land skipping the finalL.

Every iteration of the corner rotator exchanges UFR and DFR, and repeating it 6 times returns the cube to exactly where it was. Step 6A will use the corner rotator 2 times if the top color is on the right side of the UFR corner, but 4 times if it is on the front, in which case it is faster to do the reverse sequence 2 times:Step 3 - making it faster:reverse corner rotator:D- R- D RStep 3 - why it works:

- Step 3A affects only 4 corners by exchanging the two front right corners and also exchanging the two back down corners.

- Doing Step 3A twice leaves corners in the same positions, except those four corners are rotated, and doing Step 3A six times leaves the corners the same as when you started.

- On the up layer Step 6 only modifies the front right corner.

- Since Step 3 started with the down layer correct, once three of the four up corners have been fixed, fixing the fourth up corner must leave the down layer correct. This is because when at every 6th move the two back bottom corners are correct, all that is left that could be incorrect are the two front right corners, but due to parity considerations, a completely solved puzzle except for two adjacent rotated corners is not possible.

- This transformation also works for a Rubik 3x3x3 cube (and is the last step of the layer by layer solution presented on that page). The only edge pieces that are affected are FR, RD, BD, which are on the lower two layers; they return back to where they were after 6 moves.

Solve the down layer.Step 1.

If possible, rotate the up layer to be correct, except some corners may by be rotated; otherwise, mix up and go back to Step 1 using a different color on the bottom.Step 2.

Fix the up layer so all corners are rotated correctly:Step 3.Reposition the cube so the up front right corner is not correct, and repeat these two steps until all up corners are correct:

- Repeat until the up front right corner has the correct color on top:

(R- D-) (R D)

WhereRandDmean to rotate the right and down layers 90 degrees clockwise, orR-andD-mean to rotate the right and down layers counterclockwise.

- Rotate the top layer 90 degrees counterclockwise.

The randomized solution described on the previous page, that simply hopes for the 1 in 6 chance to skip Step 2, can be a bit unsatisfying. It's not hard to learn the sequence of Step 2, but it is interesting to note that you don't have to. Instead, we can borrow the sequence from Step 3A, which we callS, and its reverseS-:Consider interleaving a do-nothing sequence ofS = (R- D-) (R D)

S = (D- R-) (D R)U's into a do-nothing sequence ofS's:

Here is how this sequence cycles three corners A,C,D on the top layer (and the cube is returned to where it was if you do it three times), or if it is followed by aU, it exchanges two corners B and C on the top layer (X denotes the corner below A at the start):

Although the sequence is relatively long when eachSis expanded to the corresponding four moves, once you understand howSworks, it is easy to remember this alternate Step 2:2 (alternate).Fix the up layer so all corners are rotated correctly:LetSbe the sequence of Step 3A. Below isS S S- S-interleaved withU U U; use it to keep the up left front corner and cycle the others, or to exchange the two up left corners, follow it with a^{2}U:S U S U S- U^{2}S-

The booklet that comes with theHomer Simpsonversion describes a three step solution using these sequences:

WWith the notation from the preceding page (where 2 means do it twice), these transformations can be expressed as:

Step 2:FRD <-> BLD:F L D L- D- F- D-("diagonal swapper")

FRD -> BLD -> BRD -> FRD:B L D L- B- L D- L-("shunter")Step 3:FRD-, BRD-, BLD-:R- D- R D- R- D2 R D2("shifter")

The 3-step solutions presented on the preceding pages employ transformations that may have to be used several times.Jaap's Pagepresents a solution that uses fewer moves by employing a different transformation for each of the possible situations that may occur.

Notation:R (right), F (front), and D (down) for 90 degree clockwise rotations of those faces, and - for counterclockwise instead of clockwise. A 2 means do it twice. Corners are denoted with three letters (e.g., BLD = back left down corner).

Sequences for exchanging corners:FLD <-> FRD:F D F- D- R- D- R

FRD <-> BRD:R F D F- D- R- D-

(Jaap's page does FRD <-> BLD:F- R- D- R D F D-)Sequences for rotating corners (+ / - denote clockwise or counter clockwise):FLD-, BLD+:These transformations are done from the point of view of the top layer solved and then solving the bottom layer, because it makes the puzzle easier to hold with the left hand and manipulate with the right hand (no moves of the up, left, or back layers needed).R- D- R F- D R- D R D2 F2

FLD+, BLD-:F2 D2 R- D- R D- F R- D R

FLD-, BRD+:R2 D- R D2 R- D2 R D- R2 D

FRD-, BRD-, BLD-:R- D- R D- R- D2 R D2

FRD+, BRD+, BLD+:D2 R- D2 R D R- D R

FRD-, BRD+, BLD-, FLD+:R2 D2 R D2 R2 D

FRD+, BRD-, BLD-, FLD+:R D F R2 D2 F2 D F- D R2

Jaap's Page presents the above transformations along with many more, including transformations to make specific patterns.

Plastic, stickerless, made in China, purchased from Amazon.com in 2015.

(DaYan, sold byMaxin, comes in a fitted box, 1.8" square)

In the early 2000's, smoother working versions of Rubik's 2x2x2 were widely available, with screws / springs for adjustable tension and smooth turning even when layers are not exactly aligned (beveled interior corners in conjunction with the spring action give a minimal degree of automatic alignment). Even dimension Rubik cubes, of which the 2x2x2 is the smallest, don't use a central axis like standard odd dimension designs such like theRubik's 3x3x3cube. Here are photos of the one shown above apart:

The Darth Maul figure is large (4 inches high) with a smooth mechanism. The others are small (between 2.25 and 2.5 inches high) from Kellogg's cereal boxes in the 2002 time frame; each has two related star wars episode II figures, one on each side.

Darth Maul

Darth Vader / Anikin Skywalker

Obiwan Young / Obiwan Older

Lea / Amidala

Dooku / Emperor

Trooper / Jango

R2D2 - C3PO

Homer Simpson

(circa 2000, 5")

Bart Simpson

(circa 2000, 4.5")

Dog, Kitty, Penguin

(China, 2006, all three are 4.25")

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube2.htm

Rubiks.com booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx

Rubiks.com assembly diagram, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx

Rubik Patent, from: www.uspto.gov - patent no. 4,378,117

Li Patent, (Eastsheen Mechanism), from: www.uspto.gov - patent no. 5,826,871

Patermann EP Patent (Mickey Mouse), EP712,649.

Khoudry International Patent (K-Ball), IP25874.

Kremmer Patent (Darth Maul), from: www.uspto.gov - patent no. 6,217,023

Nicholas Patent (uses magnets), from: www.uspto.gov - patent no. 3,655,201

Patent filed by Erno Rubik 1975, sold by Ideal Toys in the 1980's.

(plastic with colored stickers, 2.2"; keychain 1.2")

The first puzzle of this type in a large class of puzzles in the years to follow. Challenging and fun to play with. A number of ways to construct this puzzle have been devised over the years; here are the pieces of an original Rubik's Cube like shown above, where there is a central axis assembly and 20 pieces that interlock with it.

- Solve the top layer (all of it, including the sides), and turn the cube over so now it the bottom layer and the bottom third of the cube is solved (easy with a little practice).

- Solve the middle layer:

Rotate the middle so centers are correct, and then move edges between the up and middle layers until the middle is solved. If an edge first needs to be flipped, move it be FU and do the edge flipper sequence of Step 3 (the edge be flipped, and you can rotate the top to move it back to be FU). Parentheses are just to make the sequence easier to read.edge mover, FU -> FR:(U R) (U- R-) (U- F-) (U F)- Flip the up edges so they all have the correct color on top:

If no up edges have correct top color, first do the edge flipper. Now position the cube so UL has correct top color and UF does not, and do the edge flipper at most two times.edge flipper:F (R U) (R- U-) F-- Move the up layer edges to their correct positions:

As needed, re-position the cube and use the edge swapper sequence.edge swapper, UF<->UL:(R U) (R- U) (R U^{2}) (R- U)- Position the up layer corners:

The corner cycle sequence leaves UFR alone and cycles the other three counterclockwise. Identify one corner that is correct (but may be rotated), or if there is not one, do the corner cycle. Then re-position the cube so the correct corner is UFR, and then do the corner cycle one or two times to make all corners correct.corner cycle:(U R) (U- L- ) (U R-) (U- L)- Rotate the up layer corners (read this whole step before starting it):

*** Don't worry that the bottom is mixed up as you do this, it will be ok in the end.

Position the cube so UFR is not correct and repeat these two steps until all corners correct:

- Repeat the corner rotator until the UFR corner is correct:

corner rotator:R- D- R D

- Rotate the up layer (
not the whole cube) so that UFR is incorrect.

Each sequence has a natural rhythm, but an easy mistake is to start off wrong. The Edge Mover and Corner Cycle start withU, the Edge Flipper (after parking theF) and the Edge Swapper start withR. To avoid forgetting your place, run the sequence in your head, and when you get faster, simply count 1,2,3,4,... as you go; 8 for the edge mover, edge swapper, and corner cycle; 4 between the F's of the edge flipper; 2 sets of 4 for the corner rotator.

Edge Mover (for Step 2):edge mover, FU -> FR:(U R) (U- R-) (U- F-) (U F)

It starts with aU, and every other move involves aUorU-.

First two moves and last two moves are clockwise, middle four moves are counter clockwise.

First 4 moves involveR, second 4 moves involveF.Edge Flipper (for Steps 2 and 3):edge flipper:F (R U) (R- U-) F-

"Park" the front withF, do(RU) (R-U), and then "unpark" the front withF-.Edge Swapper (for Step 4):edge swapper, UF<->UL:(R U) (R- U) (R U^{2}) (R- U)

It'sR R- R R-interleaved withU U U. The^{2}UR's alternate + and -, and theU's keep going clockwise, where the third is 180 degrees.Corner Cycle (for Step 5):corner cycle:(U R) (U- L- ) (U R-) (U- L)

It'sU U- U U-interleaved withR L- R- L.Corner Rotator (for Step 6):corner rotator:R- D- R D

Always complete this sequence before doing Step 6B; it is easy to forget the finalDwhen you see the correct color on top.

It will be done twice (eight moves to rotate once) or 4 times (16 moves to rotate twice).

Step 1:Pick a color for this face that is easiest to locate quickly (e.g. white). Some people like to work from one corner, placing adjacent squares one at a time. Others like to solve the top edges first (forming a cross) and then it is easy to rotate the corners up.

Step 2:Instead of using the edge flipper, learn the symmetric sequence that moves an edge down counterclockwise from up to middle:edge cc-mover, UF -> MLF:(U- L-) (U L) (U F) (U- F-)Step 3:Before the finalF-, if the right side of FR is not the top color, instead of wasting time to doF- F, repeat the(R U) (R- U-)before doingF-.

Step 4:If more than two edges need to be exchanged, rotate the top layer so the UF edge is correct and just do the first 7 steps of the edge swapper. Omitting the last move of the Edge Swapper leaves UF unchanged and cycles the other three counterclockwise. So you are done if that was needed. Otherwise, it turns out that now a second edge swapper operation, possibly followed by aU-, will always suffice. However, if you are willing to remember yet another sequence, a second edge swapper operation can be avoided for the case that a clockwise cycle is needed by using this sequence:clockwise cycle UL, UB, UR:(R U^{2}) (R- U-) (R U-) R-Step 5:If no corners are correct, learn how to tell for which orientation of the cube the corner cycle will leave things so that a counterclockwise cycle will be needed. Or, if you have identified a correct corner and a clockwise cycle of the other three is needed, instead of doing the corner cycle twice (three times returns the cube to where it was), save time by reversing the sequence:reverse corner cycle:(L- U) (R U- ) (L U) (R- U-)Step 6:Every iteration of the corner rotator exchanges UFR and DFR, and repeating it 6 times returns the cube to where it was. Step 6A will use the corner rotator 2 times if the top color is on the right side of the UFR corner, or 4 times if it is on the front, in which case it is faster to do the reverse sequence 2 times (easy, start withD-instead ofR-and everything follows):reverse corner rotator:D- R- D R

Step 6 is the same as Step 3 of the solution presented forRubik's 2x2x2, and we repeat here the observations from that page:

- Step 6A affects only 4 corners by exchanging two front right corners and also exchanging the two back down corners.

- Doing Step 6A twice leaves corners in the same positions, except those four corners are rotated, and doing Step 6A six times leaves the corners the same as when you started.

- On the up layer Step 6 only modifies the front right corner.

- Since Step 6 started with the down corners correct, once three of the four up corners have been fixed, fixing the fourth up corner must leave the down layer correct. This is because when at every 6th move the two back down corners are correct, all that is left that could be incorrect are the two front right corners, but due to parity considerations, a completely solved puzzle except for two adjacent corners is not possible (however, although not hard to overcome, this is not true for the
Rubik 3x3x3 Void Cube).

- The only edge pieces that are affected are FR, RD, BD, which are on the lower two layers; they return back to where they were after 6 moves.

A completely solved 3x3x3 cube except for two adjacent corners exchanged is not possible due to parity considerations; that is, if just two adjacent corners are interchanged, then it must be that the edges are not completely solved. However, this is possible for theRubik's 2x2x2cube.

If you are fast with the Step 5 corner cycle sequence, and don't want to bother remembering the sequence to exchange two corners of a 2x2x2 cube (which corrupts edges when used with the 3x3x3 cube), Steps 1, 5, and 6 will solve the 2x2x2 cube, by using the corner cycle appropriately for Step 5:

The single swap is all that is needed, since it can be used 3 times for a diagonal swap and twice for a double swap. However, by using all three variations shown above, it is at most 9 moves for a single swap (8 moves for the corner cycle plus the finalU) or 16 moves for the diagonal or double swap. Note each time a corner sequence or reverse corner sequence is done, the cube first needs to be repositioned so that the corner that does not move is in the UFR position. If you don't want to remember the reverse corner cycle, the second sequence of the double swap can be a standard corner cycle on D,B,A followed by aU; however, counting that final^{2}Uas two moves, it is no fewer moves than doing two single swaps.^{2}

Here is a different approach that starts with solving the corners, then the top and bottom edges, and finally the middle edges.

1.Solve the corners using a solution forRubik's 2x2x2.

2.Position up and down edges by moving to and from the middle layer:

- Cycle edges between the middle and up layers to get three top edges correct:

RB -> FU, FU -> FD, FD -> RB:F M F-

That is, repeatedly position the cube so that the edge to be moved is RB, rotate the U layer so that where you want to move it to is FU, and cycle.

- Turn the cube over, and repeat Step A.

- Move the edge that goes to FD to the FU position; then move final edge to FU.
3.Use this to flip up and down edges:Flip the UF edge:F- M (F M)^{2}F-4.Use rotations of the middle layer and these to position middle edges:Front back swap,LF <-> LB, RF <-> RB:(R^{2}M^{2})^{2}

Clockwise cycle,RF -> LB -> RB -> RF:R^{2}M R^{2}M-5.Use this to flip middle edges (for right to left diagonal, do B2 before and after):Flip MRF and MRB:(R M-)^{3}R M^{2}R (M- R)^{3}

Plastic, stickerless, made in China, purchased from Amazon.com in 2015.

(left:Newisland, sold byYaMiYo, comes in a with a storage bag, 3.25" square;

right:DaYan, sold byMaxin, comes in a fitted box, 2.3" square)

In the early 2000's, smoother working versions of Rubik's 3x3x3 were widely available, with screws / springs for adjustable tension and smooth turning even when layers are not exactly aligned (beveled interior corners in conjunction with the spring action give a minimal degree of automatic alignment). TheNewislandcube shown above was a gift from a friend who does speed cubing; it is smooth and quiet, comes with a storage bag and directions, and its literature explains PA plastic lower resistance, anti-popping, and internal construction. The less expensiveDa Yancube shown above has different but similar construction; here are photos of it apart:

Besides more complex insides that include screws and springs, magnets have been used to give a nice click stop effect. It not only is a beautiful cube that is fun to use, but is preferred by some who do speed cubing.

"Valk 3", designed by Mats Valk, purchased from Amazon.com 2017.

(plastic, 2+3/16" square;

comes in a sturdy 3.75" square box with a magnetic lid

and a compartment in the bottom with extra stickers and springs)

The original Rubik cube as well as modern versions are all based on a center spindle assembly that connects the six center squares and holds the whole cube together where the other pieces flow around it.

TheRubik 3x3x3 Void Cubeis based on a completely different idea. There are no centers (one can pass their finger through the cube in all three directions).

TheRubik 3x3x3 Edges Only Cube(a.k.a. cornerless void cube) uses the same mechanism and eliminates the corner pieces as well.

One way to measure large is the dimension of the cube; for example cubes of size 33x33x33 have been made. But another measure is the physical size of the cube. This cube, made by Tony Fisher, is 1.57 meters (over 5 feet) tall:

McDonalds, 2.2"

Chex Cereal, 2.2"

Jack Daniels, 2.2"

UPS, 2.2"

Mickey Mouse, 2.2"

MatLab, 2.2"

Small Cube, 1.2"

Small Shiny Cube, 1.2"

Dice made by Volker (Germany), 2.2"

Assembly Cube, 2.2"

Beust's Page, from: http://beust.com/rubik

Bieber's Page, from: http://www.ronaldbieber.de/Fun/Rubik

Chess And Poker Page, from: http://www.chessandpoker.com/rubiks-cube-solution.html

Cheyer's Page, from: http://www.ai.sri.com/~cheyer/rubiks/rubiks.html

Dedmore's Page, from: http://www.helm.lu/cube/solutions/rubikscube

Dry Erase Board Page, from: http://www.thedryeraseboard.com

Fridrich's Page, from: http://ws2.binghamton.edu/fridrich/cube.html

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube3.htm

Jasmine Page, from: http://peter.stillhq.com/jasmine/rubikscubesolution.html

Jeays' Page, from: http://jeays.net/rubiks.htm

JJuergen's Page, from: http://www.mathematische-basteleien.de

Marshall's Page, from: http://helm.lu/cube/MarshallPhilipp

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rc/RubCub0.htm

Monroe's Page, from: http://www.alchemistmatt.com/cube/rubik.html

Nerd Paradise Page, from: http://www.nerdparadise.com/puzzles/333

Olefsky Puzzle Solver Page, from: http://www.puzzlesolver.com

Ortega and Jelinek Corners First Solution Page, from: http://rubikscube.info/ortega.php

Oxford ComLab Text Solution, from: ftp.comlab.ox.ac.uk

Petrus' Page, from: http://lar5.com/cube

Rob's Rubik Repair Page, from: http://www.roobik.com/cgi-bin/rubix/rubix.cgi

Rubiks.com Solution, from: http://www.rubiks.com

Scared Cat Page, from: http://www.scaredcat.demon.co.uk/rubikscube/the_solution.html

Shengshou Speed Cube Solution, from: http://www.speedsolving.com/wiki/index.php/Shengshou

Shon's Rubik's Place Page, from: http://www.rubiksplace.com

Still's Page, from: http://peter.stillhq.com/jasmine/rubikscubesolution.html

You Rubik Page, from: http://www.yourubik.com

WikiHow Page, from: http://www.wikihow.com/Solve-a-Rubik's-Cube-(Easy-Move-Notation)

Rubik Hungarian Patent, BE887875.

Rubik U.S. Patent, from: www.uspto.gov - patent no. 4,378,116

Sugden Patent, from: www.uspto.gov - patent no. 6,974,130

Sugden Design Patent, from: www.uspto.gov - patent no. D495,378

Scott Patent Application, from: www.uspto.gov - application no. 2010/0230897

God's Number is 20, from: http://www.cube20.org

Kociemba's Two Phase Algorithm and Cube Math, from: http://kociemba.org/cube.htm

22 Moves, from: http://www.springerlink.com/content/q088143tn805k124/fulltext.pdf

Speed Solving Page, from: http://www.speedsolving.com/wiki/index.php/Main_Page

Superflip, from: http://www.speedsolving.com/wiki/index.php/Superflip

Rubiks.com Page, from: http://www.rubiks.com

Rubiks.com Booklet, from: http://www.rubiks.com

Rubiks.com Diagrams, from: http://www.rubiks.com

Rubiks Cube Typesetting with TeX, from: http://www.ctan.org/pkg/rubik

Cube Lovers Archive, from: http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers

Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik%27s_cube

Wikipedia - God's Algorithm, from: http://en.wikipedia.org/wiki/God%27s_algorithm

Wikipedia - solutions, from: http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik's_Cube

Made by SOCUBE, Kuala Lumpur, Malaysia, 2009.

(plastic, 2.1 x 2.1 x 1 inch;

white opposite yellow, red opposite orange, blue opposite green)

Availabe at McDonalds in the U.K. 2002.

(plastic, 3.5 inches)

A very easy (but cute) puzzle.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/morph.htm

Purchased 2012.

(plastic, 3.9" x 1.5" x 3/4" inches)

A mechanically fun and not too hard puzzle, although the graphics can make it confusing to look at it mixed up and determine what needs to be done.Jaap's Pagepresents a solution that first solves the edges and then the corners.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/index.htm

Rubik 1x2x9 "Chopsticks",

designed by Oskar Van Deventer and Ola Jansson, sold by Mefferts 2013.

(plastic, 5+1/8" x 1+7/8" x 1+3/8")

A longer puzzle in the theme ofRubik 1x2x5. Shown above is the puzzle and it turned over.

a.k.a.Unlucky Twist

Designed and custom made by Oskar Van Deventer, 2013.

(plastic, made with a 3D printer, 10.25" x 1.5" x 3/4")

A larger version of the mass producedRubik 1x2x9. Here are photos of successive manipulations, where the third photo is a close up of the center of the second one to see how the mechanics of how the layers build out from the middle cube:

Designed by Katsuhiko Okamoto 2007, purchased from Gentosha, Japan, 2009.

(plastic, 2.25 by 2.25 by 3/4 inches;

by the same designer as theRubik 3x3x3 Void Cube)

Seems to impossibly stay together as sets of three are flipped:

Notation:L (left), R (right), F (front), B (back) denote flip that side.

Jaap's Pagepresents a computer analysis that shows there are only 192 reachable positions, each requiring at most 8 moves to solve. By just playing with this puzzle it usually does not take very long to solve, or to get it to where it can be fixed with the following simple transformation:

F R F R F R

(flip two adjacent edges)

The directions that came with the puzzle also present the following transformations (after doing the last two, rotate or turn the puzzle over to get the views shown):

L F L R B R

(flip two opposite edges)

L F L R F R

(exchange opposite edges)

F L R B

(flip center and

exchange two opposite edges)Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/floppy.htm

a.k.a.Magic Floppy Cube

Made in Hong Kong, 2009.

(plastic, 2.25 by 2.25 by 3/4 inches)

A version of theRubik 1x3x3 Floppy Cubewhere the cube sizes progress from small to large in both horizontal dimensions; it can be solved in exactly the same way. Fun shapes can be formed:

Unlike theRubik 3x3x3 Mirror Cubewhich progresses in all three dimensions, here all cubes have the same thickness and not all unsolved positions have a jumbled shape. In fact, because for this puzzle it is very easy to get back to the square shape, it is perhaps even easier to solve than the normal floppy cube. By randomly mixing and restoring to a square the puzzle is typically quickly solved or in a position where two adjacent edges are flipped, which can easily be fixed with the following transformation (F and R denote flips of the front and right sides, 3 means do it three times):

(F R)^{3}

Designed by Katsuhiko Okamoto, made by Gentosha, Japan, 2010.

(plastic, 2.25 by 2.25 by 3/4 inches)

A generalization of the Rubik 1x3x3 Floppy CubeRubik 1x3x3 Floppy Cubewhere a 1x1x2 portion can rotate (see also theRubik 1x3x3 Floppy Mirror Cube); here are a sequence of three moves to make an edge piece sit up:

Jaap's Pagepresents an analysis, but by just playing it is relative easy to solve, and it is easy to make interesting shapes, like the one on the left below, and then return the puzzle to flat.

Notation:L (left), R (right), F (front), B (back) denote flip that side, L90 to turn the left side 90 degrees clockwise, B90 to turn the back side 90 degrees clockwise.

Once flat, moves for the 1x3x3 Floppy Cube can be used to solve or to be left with one edge flipped as shown on the right above. To fix this, make the edge opposite to this edge sit up, then use the edge pair flipping transformation from the 1x3x3 Floppy Cube (LFL RBR), and then put the opposite edge back down; all 90 rotations are in pairs, so all movement can be clockwise:L90 B90 L90 L F L R B R L90 B90 L90

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/floppy2.htm

Made by J. A. Storer from a standard Rubik 2x2x2 cube, 2007.

(two brass plates glued to a Meffert's Eastsheen Rubik 2x2x2 cube, 2 inches)

This is a relatively easy puzzle that can usually be solved without too much effort by playing a bit. However, it can get more mixed up than is first apparent. An organized way of solving is to combine repositioning of the bandaged portion with transformations for the standardRubik's 2x2x2 cubethat only use R and D rotations, such as these which are shown onJaap's Page.

Notation:R (right) and D (down) for 90 degree clockwise rotations of the corresponding faces, - to do counterclockwise instead of clockwise, and 2 to do it twice; corners are denoted with three letters (e.g., FLD- = counterclockwise rotation of the front, left, down corner).FLD-, BRD+:R2 D- R D2 R- D2 R D- R2 D

FRD-, BRD-, BLD-:R- D- R D- R- D2 R D2

FRD+, BRD+, BLD+:D2 R- D2 R D R- D R

FRD-, BRD+, BLD-, FLD+:R2 D2 R D2 R2 D

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube2.htm

Made by J. A. Storer from a standard Rubik 2x2x2 cube, 2007.

(four brass plates glued to a Meffert's Eastsheen Rubik 2x2x2 cube, 2 inches)

This is an easy puzzle, but still fun, that can be solved without too much effort by playing a bit.

a.k.a.Rubik 2x2x2 Super Square

Made in China, 2010.

(plastic, 2.2 inches)

Works like aRubik 2x2x2, and also each face has a circle that rotates. So this puzzle is a bit like a 2x2x2 nested inside a standard 2x2x2 cube.

Two, three, or four Rubik's 2x2x2 cubes joined, purchased from UK3 2005.

(plastic, each formed from 7/8 inch 2x2x2 cubes inches)

a.k.a.Slim Tower, Franken Tower

Made by Gentosha, Japan, 2009.

(plastic, 1.5 x 1.5 x 2.25 inches,

opposite red is yellow, opposite blue is light green, and opposite gray is black)

An extended Rubik's 2x2x2 where two dimensions are restricted to 180 degree rotations.

Notation:With a 2x3 surface facing you, F (front), B (back), U (up), and D (down) denote 180 degree clockwise rotations of the corresponding faces, L (left) and R (right) denote a 90 degree clockwise rotation of the corresponding faces, - to rotate counterclockwise instead of clockwise, 2 or 3 to do it two or three times.

Solution:The solution that comes with the puzzle gives the following transformations that may be used to solve the corners and edges independently.Solve the corners using the following transformation as needed:BRU <-> BRD:Solve the edges using the following transformation as needed:U F R F L- U L U R- U RUF <-> UB:(U R2)^{3}

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube223.htm(Presents a similar approach with many additional transformations.)

Made in Japan, purchased from Mefferts 2010.

(plastic, 1.7" x 1.7" x 3.4"

green opposite yellow, red opposite orange, white opposite blue)

UnlikeRubik 2x2x3, 90 degree turns on the long dimension can lead to jumbled shapes; here is a sequence of three 90 degree turns:

Solution

1. Return the puzzle to the correct shape.One approach is to think of this as a 2x2x2 cube formed by the center portion with stuff hanging off of it, and employ2. Use a solution forRubik 2x2x2transformations.Rubik 3x3x4.(Steps to correct edge pieces can be omitted).

a.k.a.Rubik 2x2x4 Super Square

Made in China, 2010.

(plastic, 2.2 inches)

The middle portion is just like aRubik 2x2x2 Nested, (where each face has a circle that rotates), and then this puzzle has a standard layer added to the top and bottom.

a.k.a.Overlap Cube

Designed by Oskar Van Deventer, purchased from Shapeways 2013.

(Lots of little uncolored plastic pieces in a 3.5" by 5.5" plastic bag;

buyer must color and assemble to have a puzzle as shown in the pictures above

from the Shapeways web page; good luck!)

Designed by Erno Rubik 1983; left purchased circa 1985; right purchased 2009.

(plastic, 1.5 inches high by 2.25 inches square)

Put the numbers in order on both sides.

Notation:R for a flip of the right side, U, D for clockwise rotations of the up and down faces (- for counterclockwise, and 2 to do it twice). We also use M to denote rotating the whole puzzle 90 degrees clockwise (with respect to looking down), as a convenience so that only right flips are needed (easier to hold and also useful for the solution toRubik 3x3x4).

Move pieces to their correct layers:

1. Repeatedly position pairs of edges on the wrong layers on the right and do R.

2. Repeatedly position two corners on the wrong layers at the front right and do:Exchange UFR and DFR:R U R U- RSolve the two layers independently:

3. Use this to permute corners; X = Step 2 transformation, Y = reverse of X:4. Use this to permute edges:Exchange URF and URB:X M- Y D-Exchange UF and UR:(R U)^{2}(R U2)^{2}XJaap's Pagepresents the transformations above (and others), as well as the following transformation to change a side to its mirror image (F denotes a front flip):

R F T- F T2 R (T F)2 T2 R T- F RFurther reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/domino.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rdml/rubdom1.htm

Made in China, purchased 2010.

(plastic, 1.5 inches high by 2.5 inches diameter)

A smaller version ofRubik3x3x3 Layeredand mechanically the same asRubik2x3x3, but with each layer being a single color (and this version has been made in a circular shape).

Although any solution for Rubik's 2x3x3 could be used, the puzzle is much easier to solve. It is easy to flip the sides as needed to make the centers match the edges (i.e., each side has a cross of a single color). Then corners can be fixed with just 180 degree rotations of the front (F) and clockwise or counter-clockwise rotations of the top (^{2}U,U-). If you want to memorize a simple transformation, this one exchanges the front top left corner with the front bottom left corner:After the above transformation has been used to fix pairs of corners, such shown below on the left, a flip of the front and back sides followed by a flip of the left and right sides gives the checkerboard pattern shown below on the right.F^{2}U F^{2}U- F^{2}

Made in China, 2012.

(plastic, 2.8" x 2.1" x 1.4" inches)

The shape can change quickly. Here are three successive moves; the first turns the back face 90 degrees clockwise, the second turns left and right two halves 180 degrees with respect to each other, and the third turns the front face 90 degrees counter clockwise:

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube234.htm

a.k.a.WitEden 2x4x4

Purchased from Mefferts, 2013.

(plastic, 2.7" x 2.7" x 1.75";

white opposite yellow, green opposite bule, orange opposite red)

The top and bottom layers can rotate 90 degrees; the other rotations are limited to 180 degrees.

a.k.a.Yong Jun Cube

Purchased from Yong Jun Toys / Mega House, 2009.

(plastic with silver stickers, 2.25 inches)

A version of the standardRubik's 3x3x3 cubecube where the cube sizes progress from small to large in all three dimensions. Each piece is distinguished by its shape rather than it color. Here are photos of three successive moves:

Any solution for the standard Rubik's 3x3x3 Cube can be used, although it may be more confusing to identify each piece based on its shape when the puzzle is mixed up than it is to look at colors on a standard cube.

Designed by T. Fisher, purchased from Mefferts 2009.

(plastic, 2.2 inches;

silver opposite gold, green opposite blue, red opposite orange;

also made with a black body)

Works just like a a standardRubik's 3x3x3 Cube, but can be confusing when the shape becomes very jumbled. Meffert's also made this puzzle in all silver and all gold, and versions from China were sold as the "Square King":

Here are photos of 4 consecutive moves:

a.k.a.Holey Cube

Designed by Katsuhiko Okamoto 2007,

top by Gentousha 2009 and uses stickers,

bottom two purchased from CubeFans 2009 and are all plastic.

(plastic, 2.25 inches;

top: gray opposite black, red opposite yellow, blue opposite light green;

bottom: green opposite blue, yellow opposite white, red opposite orange)

By the designer of theRubik 1x3x3 Floppy Cube. Logically the same as the classicRubik's 3x3x3 Cube, but mechanically very different. The standard Rubik's 3x3x3 cube relies on central 3D axes to which the centers are attached and the other pieces flow around. Here, one can look through the center of the cube along any of the three axes (i.e., a square bar with a 1x1 unit cross section can be passed through the cube in any of the three directions). Solving is the same as the standard version, except for the void cube parity issue, described on the following page.

In a standardRubik's 3x3x3 Cube, not all possible positions are reachable by mixing up the puzzle. For example, it is not possible to end up with the cube solved, except for two adjacent corners exchanged. Note that this fact is not at odds with such a situation being possible for theRubik's 2x2x2 Cube, which has no middle layers. For example, cycling the UFL, UBL, UBR corners counterclockwise followed by rotating the up layer 90 degrees clockwise results in the UFL and UBL corners being exchanged and the remainder of the 2x2x2 cube unchanged, but for the 3x3x3 cube this would leave the edges of the up layer disturbed.

Thevoid cube parity problemis when the puzzle is almost solved in an apparently impossible position. For example, using the simple layer at a time solution, as was presented for the standard Rubik's 3x3x3 cube, you may get stuck at the end with something like this:

Such a configuration corresponds to a standard Rubik's 3x3xx3 cube where in addition to the two exchanged corners, some center squares are mixed up as well. Other solution approaches could result in impossible configurations of the edges. With the void cube, there are no middle tiles to get mixed up, and some impossible positions for the standard 3x3x3 cube are now possible.

Rather that mix up up the puzzle and try again, there are many ways that have been published for fixing the problem. But without having to remember something new, a simple approach is to try to solve using whatever method you use for the standard cube, and if it works fine (you lucked out and got the right mode of parity), and if not, go back to a place where you can make a move that will change parity with respect to the center squares and resolve from that point forward.

When using the basic 6-step layer by layer solution for Rubik's 3x3x3, one can just solve as usual, hoping things will work, and if not, rotate the middle layer 90 degrees, and then resolve from that point on.

When using a corners first solution, at the last phase that solves the middle, the same sequences can be used, possibly preceded with an additional 90 degree rotation of the middle layer.

a.k.a.Cornerless Void Cub

Left: made by Smaz Smart Toy Shop IQ Toys from a Gentosha Void Cube 2009.

right: mass produced by Cube For You (C4Y) 2009;

(plastic, 2.25 inches,

left: white opposite yellow, blue opposite green, orange opposite red,

right: blue opposite green, purple opposite red, and yellow opposite gray;

left looks nice, right has a smoother mechanism)

A simplifiedVoid Cubethat removes everything but the edges from a standardRubik 3x3x3 Cube; complements theRubik 2x2x2 Cubethat removes everything but the corners.

The puzzle has exactly two solutions. To see this, observe that for each color there is exactly one other color for which it shares no edge, so this determines the pairs of colors that are opposite each other. Now choose two adjacent colors to make a standard orientation with one on the top and one on the front (for example, for the puzzle on the left above, blue on top and purple on front), which uniquely determines the bottom and back colors, and now it is possible to solve the puzzle with either choice for the left and right colors.

Although a solution for the void cube can be used here (omitting solving corners), shorter sequences can be employed because there is no need to avoid disturbing the corners when manipulating the edges.

Rubik's 3x3x3 with graphics on the middle squares, produced in 1988.

(plastic, 2.1 inches)

Many promotional versions of the standardRubik's 3x3x3cube have graphics printed on the faces that require the middle square to be properly oriented. Rubik's 3x3x3 Fourth dimension adds minimal graphics for this purpose. Here are the directions from from the box lid:

Some Rubik's solutions, such asMarshall's Page, employ transformations that preserve center orientations. For others the centers can be fixed at the end with simple moving around and rotating of the middles that does not affect the remainder of the puzzle. TheDry Erase Board Pagegives the following idea:0. Optional: Rotate an outside layer (or more than one if you want).

1. Rotate a middle layer.

2. Rotate a different middle layer.

3. Reverse step 1.

4. Reverse step 2.

5. Reverse step 0.Jaap's Pagegives specific transformations.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube3.htm

Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/333/centersolve

Marshall's Page, from: http://helm.lu/cube/MarshallPhilipp/Rubikfourth.htm

Custom made Rubik's 3x3x3, one color per layer, purchased 2006.

(plastic, 2.2 inches)

Mechanically the same as Rubik's 3x3x3, but with each layer being a single color. Although any solution for Rubik's 3x3x3 could be used, the puzzle is much easier to solve; the solution below is the same as that for theRhombi Diamond.

Solution:

1.Solve the middle layer.Easy if you don't care about the rest of the puzzle.2.Solve the top and bottom edges.Easy by using 180 degree front rotations to exchange incorrect edges.3.Solve the bottom back right and bottom back left corners.It is easy to play with top rotations and 180 degree front rotations to make at least one bottom corner red; rotate this corner to the bottom back right. If the bottom back left corner is green, play some more with these rotations to make the top front left and top front middle red, then rotate the front 180 degrees to bring these two red cubes down, and then rotate the bottom 90 degrees to bring the red corner to the back right (and making the red corner that was in the back right now in the back left).4.Solve the remaining incorrect corners.This can be done with just 180 degree rotations of the front (F) and clockwise or counter-clockwise rotations of the top (^{2}U,U-). If you want to memorize a simple transformation, this one exchanges the front top left corner with the front bottom left corner:F^{2}U F^{2}U- F^{2}

Ideal Toy Co., 1981.

(plastic 2.2 inches, with cardboard can with plastic lid)

A standardRubik's 3x3x3 Cubefor which each day of the year one can solve the top face to that day. It is much easier than the standard cube, since only one side has to be solved. For a given day, the top left and bottom right corners of the top face are blank, the top middle square hasday, the top left has one ofSun,Mon,Tues,Wednes,Thurs,Fri,Satur, the middle three squares are the month,JAN,FEB,MAR,APR,MAY,JUN,JUL,SEP,NOV,DEC, and the bottom right two squares are the date (or just the bottom right if the date is only one digit).

Here is a Dutch version Here is a Dutch version solved for Monday, Jan 1 on the left, and on the right the other three sides for this solution (in Dutch,day=dag, Sunday through Saturday areZondag,Maandag,Dinsdag,Woensdag,Donderdag,Vrijdag,Zaterdag, and January through December areJanuari,Februari,Maart,April,Mei,Juni,Juli,Augustus,September,Oktober,November,December).

a.k.a.Bicube

Made by Mefferts, 2009.

(left: plastic 2.3 inches, red opposite white, yellow opposite orange, blue opposite green;

right: plastic 1+5/8", red opposite orange, green opposite blue, yellow opposite white)

The bandages restrict the way in which aRubik's 3x3x3cube can be mixed up, and the sequences to solve it are also restricted.Jaap's Pagepresents analysis and solution sequences. Here is what the other three sides look like:

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/bandage.htm

a.k.a.Fused Cube

Made in China 2008.

(plastice, 2.2 inches)

In a theme similar toRubik's 3x3x3 Bandaged, the "patches" restrict the way in which aRubik's 3x3x3cube can be mixed up, and the sequences to solve it are also restricted. Here is what the other three sides look like:

a.k.a.Brick Cube

Made by Hidetoshi Takeji, 2008.

(plastic, 2.2 inches)

This is aRubik's 3x3x3 cubethat has been patched in pairs along two of the three dimensions; to see this, rotate the middle section by 90 degrees:

Here is what the other three sides look like:

Designed by Katsuhiko Okamoto, purchased in Japan, 2010.

(plastic, 2.2 inches square)

Like a standardRubik 3x3x3cube but movement is restricted so that a face may only turn in the direction of the arrows. When solved, all faces have consistent arrows and can rotate only in the indicated direction. When mixed up, some faces may have no arrows (and can rotate in either direction) and some faces may have arrows in both directions (and cannot be rotated in either direction). Here are box back and the other three sides:

a.k.a.TomZ Constrained Cube, Tom's Constrained Cube

Purchased from Mefferts, 2012.

(plastic 2.2" square;

TomZ Constrained Cube 90,

TomZ Constrained Cube 180,

TomZ Constrained Cube 270,

TomZ Constrained Cube Ultimate)

Locks in the center allow the corresponding face to only rotate a particular number of degrees. Below is a photo of the 180 degree cube, and also a photo of a second 180 degree cube which came with its blue face set to 90 degrees. The ultimate cube has a mixture of degrees on its faces, including 0 degrees.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/quarter.htm

Made by Cube 4 You (C4U), 2009.

(plastic, 2.2 by 2.2 by 3 inches; white body has opposite sides white / blue, red / orange, green / yellow, the same as the color scheme as the standard Rubik's 3x3x3; black body has opposite sides black / white, red / yellow, green / blue)

This extension of the standardRubik 3x3x3cube allows only 180 degree rotations in two of the dimensions. One solution approach is to think of an "outer"Rubik 2x2x3 Dominoformed by the top and bottom layers with an "inner" domino in the middle:

1. Solve the outer domino.

2. Solve the inner domino, except if your solution makes use of flips of the front, back, or left sides, replace each such flip by a flip of the right side (that is, rotate the middle layers appropriately, flip the right side, rotate the middle layers back).

3. If Step 2 ended up using an even number of flips, then the puzzle is solved. Otherwise, perform the following transformation, adapted fromJaap's Pagefor the domino, that does nothing to the middle two layers (by exchanging an upper and lower middle edge) using an odd number of flips:D2 R M- (D2 R)^{3}M R D2

Notation:R denotes a flip of the right face, M a 90 degree clockwise rotation of the middle two layers (with respect to looking down from the top), D and D- clockwise and counter clockwise rotations of the lower middle layer (with respect to looking up from the bottom), 2 and 3 mean do it two or three times.Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube334.htm(Presents a similar approach with many additional transformations.)

Designed by Aleh & Eveniy, purchased from Mefferts 2013.

(plastic 3.75" x 2.25" x 2.25";

red across from orange, blue across from green, yellow across from white)

Designed by Aleh, Tont, & Eveniy, purchased from Mefferts 2013.

(plastic 3.75" x 2.25" x 2.25";

red across from orange, blue across from green, yellow across from white)

One of a number of generalizations sold ofRubik 3x3x5. Unlike the standard 3x3x5 shape or the big brother of this puzzle, theRubik 3x3x5 Cross, the shape of the puzzle can change quickly; below are three successive 90 degree clockwise rotations:

Designed by Aleh, Tont, & Eveniy, purchased from Mefferts 2013.

(plastic 3.75"; red across from orange, blue across from green, yellow across from white)

One of a number of generalizations sold ofRubik 3x3x5. Like the standard 3x3x5 shape and the little brother of this puzzle,Rubik 3x3x5 X, the shape of the puzzle does not change as it is manipulated.

Made by WitEden, sold by Mefferts 2011.

(plastic, 2.25 inches;

WitEden made a number of variations, many sold by Mefferts,

including smaller heights, white bodies,RoadBlockversions, andCrazyversions)

Here are three successive moves (top, right, middle):

Made by WitEden, sold by Mefferts 2011.

(plastic, 2.25 inches;

a generalization of the standard3x3x9version; also sold in a white body)

Here are three successive moves (back two, middle slice, back):

Made by mf8, sold by Mefferts 2012.

(plastic, 2.1" x 2.75" x 3.5", with storage bag 7.4" x 5.75";

white opposite yellow, red opposite orange, green opposite blue)

For all three dimensions, only 180 degree turns are useful.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube345.htm

a.k.a.Rubik's Master Cube

Determine your cube color scheme:Since a Rubik 4x4x4 cube has no center squares, the first thing is to determine the color scheme of your cube (by looking at the corners and reasoning it out). Here is a diagram of the standard color scheme, which we use here:

Notation:We use the same notation as for Rubik's 3x3x3 with the additional convention that a lower case letter means move the corresponding row that is one in from that edge. For example,U, as with Rubik 3x3x3, means rotate the top clockwise 90 degrees, andumeans rotate the layer below the top (the third layer up from the bottom) by 90 degrees clockwise. We use brackets to move two rows together; for example,[Uu]denotes rotating the top half of the cube 90 degrees clockwise. In fact, if it is a dexterity challenge to move a single middle layer, an easy way to do aumove, for example, might be[Uu]followed byU-.

Basic Approach:

The following three pages described the three phases of solving:Phase 1: Match up the centers.

Phase 2: Match up the edges.After Phases 1 and 2 are completed, each face will have the correct color in the center four squares and, although the edges are in general completely mixed up, they are all in matching pairs; that is a typical face, such as the red face, might look like this:

Phase 3: Solve like a Rubik's 3x3 cube.Normal Rubik 3x3x3 moves never mess up the center groups or edge pairs (the pairs move around just like single edges do on a Rubik 3x3x3 cube). Use any layer at a time Rubik's 3x3x3 solution.

It may be that after solving, there remains a single edge pair flipped and / or exactly two corners or edge pairs exchanged (which cannot happen with a standard Rubik 3x3x3 cube), and a little additional work is done to finish up.

This can be done one face at a time (in any order) with a variation on a simple 3 move sequence. For example, if there are a pair of red squares on the front face and also a pair on the up face, then the faces can be oriented so that the pairs line up, and then do:Or suppose that the front face already has three red squares and the fourth one is on the top face:Or suppose there is a red square on the back that needs to come to the front.All three of these examples are essentially the same simple idea:Orient the cube so that the face is on front and what you want to move to the front is on the up face or the back face, then rotate the two faces so that that after the first step you will not have two squares diagonally opposite, and do:1. Rotate the right half of the cube as appropriate (or left half also works).

2. Rotate the front as appropriate.

3. Rotate the left or right half back.

Edges can be paired one at a time (in any order) by first placing two to be paired in either of the two positions shown here

then doing[Dd]if they are positioned as on the left or[Uu]if they are positioned as on the right, then doing the simple three move sequence

R U R-

and finally doing a[Dd]-or[Uu]-to restore things. The net effect is to move XX to the up-front position, and to split the pair in either the up-back position or the up-right position. So before doing this put an unmatched pair in the up-back position if it is the case on the left above or the up-right position if it is the case on the right.

At first things are slow when one repeatedly hunts for a pair of matching squares to move them into position. If when you get them in position they are not offset, it is easy to fix that; e.g.:

R U- B- R^{2}

It is not necessary to memorize this sequence; regular 3x3x3 moves never un-pair edges, and just playing around suffices to move squares around. However, it saves time to remember it.

Finally, all edges will be paired, or exactly two are not, which can be paired with this sequence:

[Dd] R F- U R- F [Dd]-

This sequence is pretty easy to remember because of its symmetry, the[Dd]and[Dd]-at each end with aUin the middle, and it isRF-to the left of theUwith the same to the right of theUexcept signs flipped to beR-F.

Step 3A:Solve as you would for a standardRubik's 3x3x3cube.*** At this point if you arelucky, the cube is completely solved!

However, there is a 50-50 chance of each of two problems:PLL parity:Exactly two corners or two edges are exchanged in and otherwise solved cube.

OLL parity:A single edge is flipped in an otherwise solved cube.Step 3B:Fix OLL parity if present.A complex sequence shown on the following page can be employed. However, at the cost of a little resolving, OLL parity can be fixed as follows with having to memorize anything new:A. Do a singlermove.

B. Use Phases 1 and 2 to fix the affected centers and edge pairs.

C. Solve as for Rubik 3x3It doesn't matter how you hold the cube when you do Step A; the flipped edge can be in the front up position or any other position. Re-solving is much less work; the left and right faces are not affected, and the front top, back, and bottom faces all have the simple pattern of 2 of the correct color and 2 of the color from the adjacent face. For example, fix the front face by doing anNote:F2followed by the standard[Rr]- F2 [Rr]sequence of Phase 1, and repeat for the top and back face (which also fixes the bottom face). Now just a few edges need to be paired up again using Phase 2.Step 3C:Fix PLL parity if present.Starting with the cube fully solved except for two exchanged edges or two exchanged corners on the up layer, this sequence will fix PLL parity leaving the bottom three layers still solved, and so all that is left is to re-solve the up layer (in fact, if it is a front back edges exchange, the up layer will also end up fully solved):This sequence is relatively easy to remember as threer^{2}U^{2}r^{2}[Uu]^{2}r^{2}u^{2}r2moves, each followed by a variation of an up two move; think of the up moves as going inward, firstU2(the outer face), then[Uu]2(the outer face and inner slice), and lastlyu2(just the inner slice).

OLL Parity is the number ofslice moves, a 90 degree turn of a single inner layer. For example bothrand[Rr]perform a slice move, but[lr]does not be becasue it comprises two slice moves,landr. It is when OLL parity is odd that we end up with a single edge flipped, something that would be impossible for a 3x3x3 cube. Here "fixing" OLL parity refers to reversing OLL parity from odd to even in order for the cube to be fully solvable.

The basic[Rr]-F2[Rr]sequence of Phase 1 and the basic[Dd]RUR-[Dd]-or[Uu]RUR-[Uu]-sequences of Phase 2 do slice moves in pairs ([Dd],[Dd]-or[Uu],[Uu]-), and so Phase 1 and Phase 2 (done in the normal way) do not change OLL parity. So after Step 3B begins with a single slice move to change OLL parity, OLL parity is not further changed. And Step 3C does not change it either since it performs an even number of slice moves. So in Step 3B, after the singlermove is done, it doesn't matter exactly how the cube is repaired so long as all slice mores are done in pairs (which is true of the straightforward implementations of Phases 1 and 2). Just don't try to get fancy and slip in an extra slice move.

It could be that Step 3B changes PLL parity. That's ok; Step 3C will fix it if needed.

Step 3B avoided having to memorize anything new to fix OLL parity. But if you like memorizing long sequences, this is a faster way to do it. Start with the cube solved as much as possible with the single flipped edge in thefront up position, and use this sequence to correct that flipped edge and leave the rest of the cube unchanged (i.e., fully solved unless there is still an OLL parity problem to be fixed). Commas and the extra spacing have no meaning other than to help reading.To make it easier to manipulate the cube,r^{2}B^{2}, U^{2}, l, U^{2}r- U^{2}r U^{2}, F^{2}r F^{2}, l-, B^{2}r^{2}randlcan be replaced by[Rr]and[Ll]. The resulting sequence shown below also fixes OLL parity, but requires re-solving the up layer. This resolving does not amount to additional work if you identify the OLL parity problem before solving the up layer (it is present if the number of the up edge pairs correctly flipped is 1 or 3).[Rr]^{2}B^{2}, U^{2}[Ll], U^{2}[Rr]- U^{2}[Rr] U^{2}, F^{2}[Rr] F^{2}, [Ll]-, B^{2}[Rr]^{2}

The terms PLL and OLL parity are standard in the Rubik's cubing literature. Parity is just a property of a current cube state that is even or odd. OLL parity is the number of 90 turns of an inner layer (a slice mover,l,f,b,u, ord), where at the end an even number is good and an odd number results in a flipped edge. PLL parity refers to a relationship between edge and corner permutations; problems can arise with even dimenson cubes where there is no center square to guide you (see also, for example, theRubik 3x3x3 Void Cubeor using a Rubik 3x3x3 solution to solve a Rubik 2x2x2 cube). Here the references to "fixing" OLL and PLL parity are just informal ways of saying that the corresponding parity needs to be reversed from odd to even in order for the cube to be solvable.

Although these parities always remain even when solving a standard Rubik 3x3x3 cube, they can become odd during the solving of a 4x4x4 cube because there is more than one visually equivalent way to configure identical pieces when forming center groups or edge pairs. For example, the figure below shows how the cube could be fully solved except for exactly two edge pairs that are exchanged (an example of a PLL parity problem). This is impossible for a standard Rubik's 3x3x3 cube but in the 4x4x4 cube, each of the two halves of two edge pairs can be exchanged independently.The complex sequences presented on the preceding page for directly solving OLL parity are fromHardwick's Page. There is much written in general about solving Rubik's 4x4x4 (and larger cubes) by reduction to 3x3x3 solving. There are also completely different approaches (e.g., layer by layer).

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube4.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rr/RubRev1.htm

Helm's Page, from: http://www.helm.lu/cube/solutions/revenge

Hardwick's Page, from: http://www.speedcubing.com/chris/4-movelist3.html

Hardwick's Speed Page, from: http://www.speedcubing.com/chris/4speedsolve.html

Jeays Page, from: http://jeays.net/rr.htm

Rubiks.com booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx

Rubiks.com assembly page, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx

Adventures In Cubing Page, from: http://adventuresincubing.com/2013/08/25/4x4-parity

Rubik's Place 4x4x4 Solution, from: http://www.rubiksplace.com/cubes/4x4

Cube Skills Rubik 4x4x4 Solution, from:

http://cubeskills.com/uploads/pdf/tutorials/beginners-method-for-solving-the-4x4-cube.pdf

Ruwix Notation, from: http://ruwix.com/the-rubiks-cube/notation/advanced

Ruwix 4x4x4 Solution, from: http://ruwix.com/twisty-puzzles/4x4x4-rubiks-cube-rubiks-revenge

Ruwix Parity, from: http://ruwix.com/twisty-puzzles/4x4x4-rubiks-cube-rubiks-revenge/parity

Speed Solve Parity, from: http://www.speedsolving.com/wiki/index.php/4x4x4_Parity_Algorithms

MZRG SiGN Notation Page, from: http://www.mzrg.com/rubik/nota.shtml

Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik%27s_Revenge

Sebesteny Patent, from: www.uspto.gov - patent no. 4,421,311

Li Patent, from: www.uspto.gov - patent no. 5,992,850

Made in China 2012.

(plastic, 2.75 inches;

blue opposite green, red opposite orange, yellow opposite white)

Here are three consecutive 90 degree turns:

Made in China 2012.

(plastic, 2.8 inches;

blue opposite green, red opposite orange, yellow opposite white)

Here are three consecutive 90 degree turns:

Made in China, 2011.

(plastic 2.3" x 2.3" x 2.9";

blue opposite green, yellow opposite white, red opposite orange)

Turns on the 4x4 planes can be 90 degrees, while turns on the 4x5 planes must be 180 degrees;Jaap's Pagepresents a solution.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube445.htm

a.k.a.TomZ 4x4x6 Cuboid

Purchased from Mefferts; made by the Now Store, Hong Kong, 2012.

(plastic, 2.5" x 2.5" x 3.5";

orange opposite red, blue opposite green, yellow opposite white)

The shape can change quickly; shown below are three consecutive 90 degree turns. Solution steps are outlined on theRubik's Ultimate Solution Page.

Further Reading

Jaap's Page,, from: http://www.jaapsch.net/puzzles/cube446.htm

Ultimate Page, from: http://rubiksultimatesolution.blogspot.com/2012/04/4x4x6-cuboid.html

Solution can work pretty much exactly the same as for the Rubik 4x4x4 solution that reduces solving to that of solving a Rubik 3x3x3; which we refer to here:

Phase 1: Match up the centers.Like the Rubik 4x4x4 solution, the same simple sequence can be used over and over to match up the center 3x3 regions. A little more organization for this process helps. Do the yellow face first, turn the cube over and do the other faces one at a time. For all but the last face, first make a column of three that passes through the center, and then for the other two columns, assemble a column of three in an adjacent unsolved face and then add it in (using the same simple sequence). The last face may end up solved after solving the second to last face, but if not and it looks like a complicated situation (e.g., just two squares exchanged between the two faces), don't worry, just perssit with the same simple sequence in different ways until you get them solved. You will likely have to mix up the second to last face as yo do this, and it may be helpful to make use of the variation where you twist the middle row along with the outer two.Phase 2: Match up the edges.Like the Rubix 4x4x4 solution, the same simple sequence can be used over and over to pair edge pieces, except now, first pair two and then pair them with the third piece. When down to the last two to be solved, the same final sequence for the last pair cane be used when the two edges are configured to look like this (where the X's are correct but the middle Y may be flipped):Phase 3: Solve like a Rubik's 3x3 cube.Solve as you would for a standardRubik's 3x3x3cube (the edge pairs and the center 3x3 squares stay together as you do the standard U, D, L, R, F, B moves). At this point if you are lucky, the cube is completely solved!

However, although the PLL parity of the Rubik 4x4x4 cube is no longer possible, OLL parity may have to be fixed. The single flipped edge triple will have a correctly oriented center piece and the two pieces to its left and right flipped. In fact, due to the presence of the correct center in a flipped triple, the presence of OLL parity becomes apparent at the end of Phase 2. For example, when referring to the figure above, either the center Y piece is flipped on the left (and things work out ok) or it is not and ends up flipped on the right.

Meffert's Page, from: http://www.mefferts.com/puzzles/profsol.html

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube5.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rp/RubPro1.htm

Monroe's Page, from: http://www.geocities.com/alchemistmatt/cube/5by5cube.html

Instructables Page, from: http://www.instructables.com/id/How-to-solve-a-5x5-Rubiks-Professor-cube

Ruwix Page, from: https://ruwix.com/twisty-puzzles/5x5x5-rubiks-cube-professors-cube

Simply Rubik Page, from: http://rubik.rthost.org/5x5x5_edges.htm

wikiHow Page, from: https://www.wikihow.com/Solve-a-5x5x5-Rubik%27s-Cube

Wikipedia Page, from: http://en.wikipedia.org/wiki/Professor's_Cube

Krell Patent, from: www.uspto.gov - patent no. 4,600,199

Li Patent, from: www.uspto.gov - patent no. 6,129,356

Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455

a.k.a.V-Cube 6x6x6

Patented by P. Verdes 2007, made by V-Cube 2008.

(plastic, 2.75 inches;

opposite black is yellow, opposite red is orange, opposite blue is green)

Uses slightly rectangular cubes on the edges and larger square cubes at the corners; works with a click-stop action. TheVerdes patentdescribes designs as large as 11x11x11. Below are photos of the this puzzle partially disassembled and the pieces that are used; note that some of these pieces are used for filling space that is not seen from the outside. The reduction to aRubik 3x3x3solution used forRubik 4x4x4andRubik 5x5x5solutions can be used for solving this cube.

Further Reading

Jaap's Page,, from: http://www.jaapsch.net/puzzles/cube6.htm

Wikipedia Page,, from: http://en.wikipedia.org/wiki/V-Cube_6

Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455

Verdes Patent, from: www.uspto.gov - patent no. 7,600,756

a.k.a.V-Cube 7x7x7

Patented by P. Verdes 2007, made by V-Cube 2008.

(plastic, 3.1 inches;

opposite black is yellow, opposite red is orange, opposite blue is green)

This cube has a slightly bulging shape. TheV-Cube 7x7x7on the left is described in the same patent as theV-Cube 6x6x6(the patent describes designs as large as 11x11x11), and like that cube, it uses slightly rectangular cubes on the edges and larger square cubes at the corners (the 7x7x7 has continuous action, whereas the 6x6x6 has click stop action).

The reduction to aRubik 3x3x3solution used forRubik 4x4x4andRubik 5x5x5solutions can be used for solving this cube.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/cube7.htm

Wikipedia Page, from: http://en.wikipedia.org/wiki/V-Cube_7

Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455

Verdes Patent, from: www.uspto.gov - patent no. 7,600,756

Made in China, 2010 - 2013.

(8x8x8: plastic, 3+1/4", red opposite orange, yellow opposite white, blue opposite green,

9x9x9: plastic, 3+3/4", yellow opposite gray, orange opposite red, blue opposite green,

10x10x10: plastic, 3+7/8", yellow opposite white, red opposite orange, green opposite blue,

11x11x11: plastic, 4+1/2", yellow opposite black, orange opposite red, blue opposite green)

The patent for theRubik 6x6x6andRubik 7x7x7cubes presented designs for up to 11x11x11 cubes. Subsequently 8x8x8 through 11x11x11 cubes were mass produced in China. The even dimension 8x8x8 and 10x10x10 cubes shown on top above are square in shape but with larger edge and corner tiles, and the odd dimension 9x9x9 and 11x11x11 cubes shown on the bottom above are also slightly curved in shape.

The reduction to aRubik 3x3x3solution used forRubik 4x4x4andRubik 5x5x5solutions can be used for solving these larger cubes.

Further Reading

Chris Hardwick's Page On Big Cube Speed Cubing, from:http://www.speedcubing.com/chris/bigcubes-info.html

YongJun MoYu 13 Layer, made in China, 2015.

(plastic, 5+1/4", over 1000 pieces, weighs 5+1/3 pounds)

This cube goes improves the 11x11x11 design with extra tabs on the ends of some pieces.Tony Fisherdoes an impressive job in a video showing a completedisassemblyof the cube, and a second video showing areassembly;he identifies38 piece classes.

Even larger Rubik's cubes have been custom made with 3D printing. In February 2011Oskar Van Deventerpresenteda Rubik 17x17x17 cube called"Over The Top"(usingShapeways3D printing technology), In 2016Coren Puzzlemade a22x22x22 cube), with 2,691 pieces, and in 2017Grégoire Pfennigdemonstrated this 33x33x33 cube with 6,153 pieces (and 6,534 stickers):

The reduction to aRubik 3x3x3solution used forRubik 4x4x4andRubik 5x5x5solutions can be used (in principle, with enough patience) for solving large cubes of any size.

Further Reading

Tony Fisher Disassemble,, from: https://www.youtube.com/watch?v=JlbsR--UVf8

Tony Fisher Reassemble,, from: https://www.youtube.com/watch?v=xP8AdF8Tl-w

Deventer presentation February 2011, from:http://twistypuzzles.com/articles/building-17x17x17/building-17x17x17.pdfShapeways Page, from: http://www.shapeways.com

Rubik 17x17x17 Video, from: http://www.youtube.com/watch?v=ihWyzvOM9pk

Rubik 17x17x17 Disassembly Video, from:http://www.youtube.com/user/OskarPuzzle?blend=2&ob=1#p/u/2/CBY7JRh2YOoRuwix Page about the 22x22x22 cube, from:https://ruwix.com/the-worlds-largest-cubic-nxnxn-rubiks-cube-puzzle-22x22x22Ruwix Page about the 33x33x33 cube,, from: https://ruwix.com/33x33x33-rubiks-cube

Greg's 33x33x33 video,, from: https://www.youtube.com/user/RubixFreakGreg

Made in China by WitEden, 2012.

(plastic, 2.25" square; white opposite yellow, green opposite blue, red opposite orange)

Looks at first like aRubik 3x3x3cube with unequal sections; but turns so as to realign the center planes in a way that causes shape to change quickly; here are three successive 90 degree turns:

Made in China by WitEden, 2012.

(plastic, 2.7" x 2.7" x 2.25"; white opposite yellow, green opposite blue, red opposite orange)

A larger version of theCamouflage Cube 3x3x3where turns realign the center planes in a way that causes shape to change quickly; here are three successive 90 degree turns:

Made by Fabio Causarano, 2007.

(plastic, 2 by 3 by 4 inches)

Constructed by combining Rubik's cube mechanisms. In only a few twists the puzzle can become quite jumbled; here is an example of a sequence of four moves:

Referring to the diagram on the right above (which uses the colorsgray,orange, andblueto denote the three portions of the puzzle), the center four gray cubes form a solid block to which two essentially separate puzzles are attached; each of the two 2x3 orange sections can be rotated (by temporarily rotating blue out of the way to solve the orange portion independent of the blue, and similarly the blue portion works independent of the orange. The colors are useful to help think about what is going on (although it is not necessarily the case that the colors will be correct whenever the puzzle has the correct shape).

Made by Fabio Causarano, 2007.

(plastic, 1.4 inches)

Like the Evil Cuboid2x3x4, constructed by combining Rubik's cube mechanisms. Here is an example of a sequence of four moves:

Made by Fabio Causarano, 2007.

(plastic, 2.2 by 2.9 by 3.7 inches)

Like the Evil Cuboids2x3x4, constructed by combining Rubik's cube mechanisms. Here is an example of a sequence of four moves:

Here is another example of a sequence of 5 moves:

Made in China, 2010.

(plastic, 1.6 inches high by 2.2 inches square,

yellow opposite white, blue opposite green, red opposite orange)

A smaller puzzle in the theme of theCrazy Cube 3x3x3. Each side can be flipped 180 degrees as in a standardRubik 2x3x3. cube. In the solved state shown above with yellow on top, when grasping the bottom and rotating the top, the yellow face rotates about the center circle. After one flip of an edge, holding the bottom and rotating the top turns the entire top face as with a standard Rubik 2x3x3 cube and rotates the circle in the bottom. Each successive flip of an edge reverses the relative movement of top and bottom. That is, one full side is always connected to the center circle of the other. Here are four successive moves of flip right, rotate top 90 degrees clockwise, flip right, rotate top 90 degrees clockwise:

Crazy Cube Mars, purchased from Mefferts, 2010

(plastic, 2.2 square, white opposite yellow, blue opposite green, orange opposite red;

Crazy Cube 2x3x3is a smaller puzzle with this theme)

There are two types of faces:The Mars member of a series of eight (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune) that differ in the configuration of the faces; it has the following face configuration:Spin Around:The circle in the center stays fixed and the remainder of the face rotates.

Spin Together:The entire face moves, as in a standard Rubik's Cube.white = around, yellow = togetherHere is a sequence of three clockwise moves of the left, right, and top faces:

blue = together, green = around

orange = together, red = around

a.k.a.WitEden Super Magic Cube

Made by WitEden, sold by Mefferts 2011.

(plastic, 2.25" x 2.25" x 1.75"; also sold in a white body)

In the same theme ofRubik's Cube 3x3x3generalized to theCrazy Cube 3x3x3, this puzzle generalizes the WitEden 3x3 stacks (that were made as large as3x3x9) to have the added movement. For this one, the circle turns with the top layer, and the bottom layer turns around the circle; a version was also made where both the top and bottom layers turn around the circle.

Made in China, 2010.

(plastic, 2.6" square, white opposite yellow, blue opposite green, orange opposite red;

Crazy Cube 2x3x3andCrazy Cube 3x3x3are smaller versions;

Crazy Cube 4x4x4 Twohas a larger center circle)

Faces rotate around the center circle; here is a sequence of three face rotations:

Here is a sequence of 4 rotations about the center:

Jaap's Pagepresents a solution.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/crazy444.htm

Made in China, 2010.

(plastic, 2.6" square, white opposite yellow, blue opposite green, orange opposite red;

Crazy Cube 2x3x3andCrazy Cube 3x3x3are smaller versions;

Crazy Cube 4x4x4Crazy Cube Two 4x4x4 has a smaller center circle)

Faces rotate around the center circle; here is a sequence of three face rotations:

Jaap's Pagepresents a solution.

Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/crazy444.htm

Designed and custom made by Oskar Van Deventer, 2012.

(plastic, made on a 3D printer, 2.3" square;

red opposite orange, yellow opposite white, blue opposite green)

The puzzle has 4 layers where the sides are yellow (front), green (left), blue (right) and white (back). Layer 1 (top) is red on top and layer 4 (bottom) is orange on the bottom. In the top layer there is a 35 tooth center gear, three 10 tooth planet gears, and 55 teeth around the edge. In the bottom layer, using finer teeth, is again a 35 tooth center gear (but of a smaller diameter than the top one), three 21 tooth planet gears, and 78 teeth on the outside. The center gears are fixed to a common axle. The axles for the top planet gears are attached to layer 2. The axles for the bottom planet gears are attached to layer 3.

Basically playing with the puzzle involves confusing rotations seeking least common multiples of numbers based on the gears. Here are general properties:

- Hold the middle two layers and rotate the top layer 7 clockwise 180 degree turns and end up with the top and bottom layers rotated 180 degrees with respect to the middle two layers.

- Hold the bottom layer and rotate the top two layers together 8 clockwise 180 degree turns and end up with layer three rotated 90 degrees clockwise with respect to the other three layers.

- Hold the top layer and rotate the bottom two layers together 18 clockwise (as you look up) 180 degree turns and end up with layer two rotated 180 degrees with respect to the other three layers (9 clockwise 180 degree turns to rotate layer 2 counter clockwise 90 degrees with respect to the top layer and rotate the bottom two layers 180 degrees with respect to the top layer).

Designed and custom made by Oskar Van Deventer, 2012.

(plastic, made on a 3D printer, 2.3" square;

yellow opposite white, orange opposite red, green opposite blue)

In the theme of the 3x3x3Gear Cub, fully functional Rubik 2x2x2 with gears. On the left below the top layer has been turned, in the middle the turning of the top has completed to make the puzzle square again, and on the right the front layer has been turned until the puzzle became square again:

Designed by Oskar van Deventer, purchased from Mefferts, 2014.

(plastic, 2.25" square;

black body: red opposite white, yellow opposite orange, green opposite blue;

white body: red opposite b;ack, yellow opposite orange, green opposite blue)

This geared 2x2 type cube allows 90 degree turns and quickly gets very messy. Starting with the orientation shown above, here is a 90 degree turn of the right side followed by a 90 degree turn of the front:

Invented by Oskar van Deventer, purchased from Mefferts, 2010.

(plastic, 2.3 inches)

Looks like a complicated version ofRubik's Cube, but is actually much easier to solve (see theGear Cube Extremefor a harder to solve version). Here is the puzzle solved, the right face rotated 90 degrees, and the right face rotated 180 degrees:

Call the operation of rotating a face 180 degrees aflip; it is theonlything you can do:

- A 90 degree rotation of a face locks up the puzzle.
- Middle layers can only be manipulated by flip operations.
- A flip cycles the adjacent middle layer by 90 degrees and rotates its 4 gear edges by 60 degrees each; 3 flips returns the adjacent middle layer to flat, and 12 flips returns you to exactly where you started. A flip also has the effect of reordering two of the gear edges in each of the other two middle layers.
- Centers move around, but gear edges of a middle layer never leave that layer.
Jaap's Pagepresents a solution. Here is an approach that requires essentially no memorization:

- Restore puzzle to be flat (easy - do flips as needed).

- Solve the corners (easy - faces cannot rotate 90 degrees).

- Use step A to solve as much as possible, use Step B, and repeat until solved (repositioning the cube as appropriate):

- Flip the right face clockwise 6 times.

(Exchanges front/rear and top/bottom of the vertical center layer).

- Flip the bottom face clockwise, flip the right face twice clockwise, flip the bottom face counter clockwise, flip the right face twice counter clockwise.

(Exchanges front/rear of vertical center layer and left/right centers.)Further Reading

Jaap's Page, from: http://www.jaapsch.net/puzzles/gearcube.htm

Invented by Oskar van Deventer, purchased from Mefferts, 2011.

(plastic, 2.3 inches)

A harder to solve version of theGear Cubewhere the edge pieces along the middle layer are not geared; shipped with stickers to go in the black U's below the gears to make a more difficult puzzle that Mefferts calls the "Gear Cube Extreme". Six turns bring the puzzle back to its shape; below are some example moves.Jaap's Pagepresents a solution.

Further Reading

Mefferts Page, from: http://www.mefferts.com

Jaap's Page, from: http://www.jaapsch.net/puzzles/gearcube2.htm

Designed by Timur Evbatyrov, purchased from Mefferts, 2015.

Another puzzle in the theme of theGear Cube.

(plastic, 2.25" square)

Designed by Oskar van Deventer and Bram Cohen, made by Mefferts 2011.

(plastic, 2.25 inches)

As shown on the left below, the puzzle spins around (keep spinning and get back to where you started). As shown in the middle below, the difficulty of this puzzle comes from its ability to be split apart along any of the three axes to allow the orientation of two halves to be changed by spinning only one half, as shown on the right below.

Designed by Oskar van Deventer, made by Witeden, purchased from Amazon.com 2014.

(plastic, 2+9/16" square)

ARubik 3x3x3cube generalized so that the middle section can turned by 45 degrees. The designer says this on the Shapeways Page:"Mixup Cube is like a Rubik's Cube, but with an unexpected twist. When a mid plane is turned by 45 degrees, other turns are possible. This way of turning mixes up the center and edge pieces. Although the concept has already been patented in 1985 by Sergey Makarov, this version has an internal 2x2x2 "cube" for extra stability."Here is a 45 degree turn of the middle followed by a 90 degree turn of the front followed by a 90 degree turn of the left side:

Further Reading

Shapeways Page, from: http://www.shapeways.com/model/31732/mixup-cube.html

Designed by Adam G. Cowan, purchased from Mefferts 2014.

(plastic, 2.2 inches, left silver edition, middle stickered edition,

right stickered version with three turns)

The Meffert's Page says"The ghost cube is an exercise in making a 3x3x3 shape modification that is as challenging as possible while only allowing one solution. Misaligned layers, odd shaped pieces, and only one color all add to the challenge."and it quotes the designer:"When I designed this puzzle back in 2008, I was inspired by Tony Fisher's Golden Cube, itself an iconic puzzle. The Ghost Cube design gradually formed over several days of 'tweaking' a basic concept until I had something really interesting. The very first prototype was printed by Geert Hellings and shown at DCD 2008 with good reviews, and early in 2009, several were made for sale by Jason Smith. After the initial sales, the Ghost Cube concept sat on the back shelf for a while, and to my surprise, several puzzle builders created their own hand made versions (including a 7x7x7 version!). Suddenly there was a strong desire to produce this puzzle, and I set to work on an injection molded production design. I am very happy with the results, and glad that I will be able to share this puzzle with the entire puzzle community! Enjoy!"

Designed by Justin Eplett, purchased from Mefferts 2013.

(plastic, 2.25" square; smooth mechanism;

left 2 color version, right 4 color version)

The off-axis points of rotation combined with two sizes of cubes, allows for jumbled shapes to be formed; for example, here are three consecutive 90 degree turns:

Designed by Adam G. Cowan, purchased from Mefferts, 2010.

(plastic, 2.2 inches;

yellow opposite white, green opposite blue, orange opposite red)

This puzzle works like aRubik's 3x3x3 Cubewhere looking at each face there are three layers that can turn. Here are two views from the top of the two layers turned.

Any move makes a non-square shape, and successive moves make a completely jumbled shape. Here is a sequence of three moves, a clockwise rotation of the back layer, followed by a clockwise rotation of the front layer, followed by a clockwise rotation of the lower right layer:

a.k.a.Pyraminx Cube

Purchased from Meffert's 2007.

(plastic, 2.2 inches)

Here is a photo of the other three sides:

It can be rotated along any of the planes that passes diagonally through the cube:

Jaap's Pagecredits this puzzle toTony Durham, says that it was originally called thePyraminx Cubeby Uwe Meffert, thatDouglas Hofstadtercoined the name Skewb in a 1982Scientific Americanarticle, discusses the relationship of the Skewb to thePyraminx, and presents a solution. There are a number of variations of this puzzle, including theSkewb Diamond,Super Skewb Diamond,Skewb Ultimate,Skewb Kite,3D Skewb, andSkewb Ball

Further Reading

Meffert's Page, from: http://www.mefferts.com/puzzles/skewbsol.html

Jaap's Page, from: http://www.jaapsch.net/puzzles/skewb.htm

McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/Skewb.htm

Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/skewb/solution

A Cubist Page, from: http://www.acubist.com

Augmented Faces Skewb

a.k.a.Polymorphix Limited Edition

Purchased from Meffert's 2008.

(plastic, 2.9 inches)

Same as theSkewbwhere each face has a protruding piece on it. The colors of each of the four faces of a protrusion must match the color of the corresponding adjacent face, which gives an explicit constraint to the orientation of a face with respect to its corners.

Augmented Corners Skewb

a.k.a.3D Skewb

Purchased from Meffert's 2008.

(plastic, 2.9 inches)

Same as theSkewbwhere each corner has been replaced with a protruding piece (that has the same three colors that match the adjacent faces).

a.k.a.Void Skewb

Designed by Tony Fisher, purchased from Mefferts 2010.

(plastic, 2.2 inches)

In the theme of theRubik 3x3x3 Void Cube, same as theSkewbbut without the centers, so that one can look through the center of the cube along any of the three axes (i.e., a square bar can be passed through the cube in any of the three directions).

Designed by Tony Fisher, purchased from Meffert's, 2009.

(plastic with metallic finish, 3.1 inches;

made in a number of colors in addition to gold,

including silver shown above, copper, white, black)

ASkewbmechanism with sections offset; makes a big mess when it is mixed up. In the same spirit as theRubik 3x3x3 Mirror Blockpieces of the cube are distinguished by shape rather than color.

a.k.a.Dinosaur Cube

Described in patent of J. Holloway 2000,first manufacturedin the mid 1990's,

left: custom made from aRainbow Cubemechanism by D. Calvo 2007,

middle two: sold by SMAZ 2011,

right: sold by Mefferts 2011.

(all are plastic, left 2.3 inches, others 2.2 inches,

left three: yellow opposite orange, pink opposite red, blue opposite white

right: yellow opposite white, blue opposite green, red opposite orange)

Each corner can twist. Below are photos of the other three sides and of the puzzle mixed up:

Next to the Pyraminx Duo, the Dino Cube is one of the most easy (but fun) Rubik's type puzzles. Hold the cube with one corner facing up and determine what colors must go on what faces. Start by solving just this upward facing corner. Then do the three adjacent corners to it. Finally, the corner facing down may just need to be rotated. Three-deep reasoning can be used, like "to rotate this triangle into place, I need to first rotate this corner so it doesn't get messed up (and then rotate it back afterwards), and before doing that I should rotate this other corner so it doesn't get messed up (and rotate it back afterwards)". This reasoning works because you don't care what happens to the bottom corner until the end, when it will end up solved except for rotating it.

Further reading:

Jaap's Page, from: http://www.jaapsch.net/puzzles/dinocube.htm

Holloway Patent, from: www.uspto.gov - patent no. 6,056,290

a.k.a.Black Flower Cube, Star Cube, Rex Cube

Made in China, 2010.

(plastic, 2.2 inches;

white body: yellow opposite black, blue opposite green, red opposite orange;

block body: yellow opposite white, blue opposite green, red opposite orange)

GeneralizedDino Cube, with two paths across each diagonal; here are 3 successive moves:

Designed by Oskar Van Deventer, sold by Mefferts 2011.

(plastic, 2.4 inches;

yellow opposite orange, blue opposite green, red opposite purple)

In the theme of theDino Cube, but much more complex; corners rotate in two different layers:

a.k.a.Super Cubix,Cube 21

Patented by K. Hrsel and V. Kopsky 1993, copyright Irwin Toys 1990.

(plastic, 2.1 inches)

Three layers that form a cube when solved. The middle layer has two identical trapezoid pieces that can be in only one of two states,squareornonsquare. The top and bottom each have four 60 degree corner pieces and four 30 degree edge pieces. The only moves are torotatethe top or bottom layers by a multiple of 30 degrees and to make a vertical 180 degreetwistalong thereference planethat passes through the two middle pieces. The middle can be solved independent of top and bottom. Repeating three times a twist followed by a 180 degree rotation of the top changes the state of the middle (if you don't care about disturbing the top and bottom, a single 30 degree rotation followed by a twist suffices). A twist followed by 180 rotations of the top and bottom, followed by a twist flips the middle upside-down. And we can rotate the top and / or bottom after a sequence of moves to align them with the middle. Hence, we address solving the top and bottom, without worrying about the middle.

The easier problem of getting the puzzle back to a cube shape, but with colors in any arrangement (as in the second figure above) requires no explicit memorization. Gather the 8 edges in the top to form the "flower" pattern; the figure below shows the flower on the left and patterns resulting from 4 twists. The bottom layer below the flower has all 8 corners arranged in a star, however, the four positions resulting from each of the twists all have identical patters on the top and bottom. So the rule for this sequence is "rotate along the major axis of symmetry 4 times" (shown by the dark lines). The only exception is when a twist gives you the same pattern back; in this case, rotate the bottom by 90 degrees before performing the twist (step 3).

Making the flower is not hard. Pairing edges and then combining pairs is the general approach, but you typically cannot avoid having two "stragglers" that are not paired. The key is to get a pair of stragglers separated by exactly two corner pieces; then you can park them in the bottom left, use rotations of the