Grand Master
With Century And A Half and Little House

Made in Asia, purchased 2007.
(felt lined wood tray and 10 wood pieces, 8 by 8.5 by 1 inches)

The directions show Red Donkey (Version C) and a number of other problems. Given the relatively large size of this puzzle, it seemed appropriate to add to these directions two puzzles with long minimal solutions.



Century And A Half
(J. H. Conway, 1978)

Little House
(Pierre-Francois Culand)

A Solution to Century And A Half
The start is the same as the Century puzzle (see Pegg's Page and Baxter's Page), but the goal is a completely specified final position (that is the start position upside-down). The name of this puzzle comes from the "pure" formulation where the central 1x2 piece is moved to the right by 1/2 unit in the start position and moved to the left by 1/2 unit in the end position; this adds two moves to this solution, to make exactly 150 rectilinear moves. Here is every 5th move of a solution of 169 straight-line moves; it employs 205 unit cost moves and it can be converted to 148 rectilinear moves by combining the moves 1/2, 5/6, 17/18, 21/22, 24/25, 28/29, 36/37, 44/45, 49/50, 58/59, 81/82, 83/84, 110/111, 114/115, 117/118, 139/140, 143/144, 148/149, 152/153, 164/165, 168/169:


(one move = slide one piece any number of units in one direction)

A Solution to Little House
Here is every 8th move of a solution to Little House of 250 straight-line moves, which can be converted to 233 rectilinear moves by combining 7/8, 41/42, 64/65, 75/76, 87/88, 91/92, 94/95, 118/119, 128/129, 134/135, 138/139, 165/166, 189/190, 192/193, 196/197, 208/209, 220/221. Positions 18 and 21 are also shown; by replacing moves 19 to 21 by two rectilinear moves, a solution results that is minimal for the straight-line and unit metrics, and only one move longer than a minimal 231 rectilinear moves solution (see the following page):


(one move = slide one piece any number of units in one direction)

A 231 Rectilinear Moves Solution to Little House
Here is every 7th move of a solution of 231 rectilinear moves solution:


(one move = slide one piece any number of units in any number of directions)


Further Reading
Pegg's Page, from: http://www.maa.org/editorial/mathgames/mathgames_12_13_04.html
Baxter's Page, from: http://www.puzzleworld.org/SlidingBlockPuzzles/4x5.htm