Century and Super-Century

Century by J. H. Conway 1975, Super Century by Gil Dogon 2004;
this puzzle formed from two 1961 Adams Co. Dad's Puzzles,
with cardboard sleeve by J. A. Storer 2007.

(cardboard sleeve, metal tray, and 10 plastic pieces, 3.75 x 3 x 5/16 inches)

The goal of both puzzles is to move the 2x2 piece to the bottom center:

Century
designed by J. H. Conway

Super Century
designed by Gil Dogon

Century Solution Idea
Century is discussed in the Winning Ways book (vol. 2) and is shown on the chart on Baxter's Page. It has a minimal soultion of 99 rectilinear moves. The article by E. Pegg gives the following solution summary:



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. This adds one initial additional move to to make exactly 100 rectilinear moves.

A Century Solution
Here is a solution of 111 straight-line moves; it can be converted to to 99 rectilinear moves by combining steps 1/2, 5/6, 17/18, 21/22, 26/27, 30/31, 52/53, 55/56, 59/60, 86/87, 88/89, and 109/110:


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

Super Century Solution Idea
Super Century is also discussed in the article by E. Pegg, and is also shown in a chart constructed by N. Baxter. Here are positions 0 (the start position), positions10, 20, 30, ..., 140, and position 150 (the end position) of a minimal straight-line solution (the complete solution is shown on the following page):


A Super Century Solution
Here is a solution of 150 straight-line moves; it can be converted to 138 rectilinear moves by combining steps 26/27, 29/30, 53/54, 56/57, 60/61, 70/71, 91/92, 94/95, 98/99, 125/126, 128/128, and 148/149:


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

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