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 Century puzzle is to move the 2x2 piece to the bottom center without regard to where the remaining pieces go. Century is discussed in the Winning Ways book vol. 2 and shown on a chart on Baxter's Page. Its name reflects a minimal solution of exactly 100 rectilinear moves formed by an initial 1/2 unit move of the central 2x1 piece followed by exactly 99 moves that end with a move of a 2x1 piece back to the middle. It is natural to consider a puzzle where the last position is fully specified; Century and a Half (also discussed in Winning Ways vol. 2) makes a vertical mirror of the start position, where its name reflects its solution of exactly 150 rectilinear moves formed by an initial 1/2 unit move of the central 2x1 piece followed by exactly 149 moves that end with a move of a 2x1 piece back to the middle.

Century

Century and a Half

The Super Century puzzle, using the same set of pieces as Century, is also to move the 2x2 piece to the bottom center without regard to where the remaining pieces go. Super Century is discussed in an article by E. Pegg and shown on a chart on Baxter's Page. It has a minimal solution of 138 rectilinear moves. Again, it is natural to consider a puzzle where the last position is fully specified. We refer to New Century as making a vertical + horizontal mirror of the start position; it has a minimal solution of 230 rectilinear moves.

Super Century

New Century

Here are every 3 steps of a 99 rectilinear steps solution (which can be converted to 111 straight-line steps by replacing with two steps each of steps 1, 4, 15, 18, 22, 25, 46, 48, 51, 77, 78, 98). This represents exactly 100 rectilinear steps when the initial 1/2 unit move is included.

Here are every 5 steps of a 149 rectilinear steps solution (which can be converted to 170 straight-line steps by replacing with two steps each of steps 1, 4, 15, 18, 20, 23, 30, 37, 41, 49, 71, 72, 98, 101, 103, 123, 127, 131, 134, 145, 148). This represents exactly 150 rectilinear steps when the initial 1/2 unit move is included.

Here are every 4 steps of a 138 rectilinear steps solution (which can be converted to 150 straight-line steps by replacing with two steps each of steps 26, 28, 51, 53, 56, 65, 85, 87, 90, 116, 117, 137).

Here are every 7 steps of a 230 rectilinear steps solution (which can be converted to 254 straight-line steps by replacing with two steps each of steps 28, 51, 53, 56, 70, 75, 79, 83, 86, 88, 91, 111, 114, 115, 141, 144, 146, 166, 175, 178, 180, 203, 205).

New Century does not end with the 2x2 piece centered at the bottom (since it produces a vertical + horizontal mirror of a start position that does not have the 2x2 piece centered at the top). However, it is natural to consider a "nice" fully specified ending position that does. One idea is ending with the two 1x2 pieces replacing the 2x2 piece:


Super Century 198

Here are every 10 steps of 198 rectilinear steps for Super Century 198 (which can be converted to 217 straight-line steps by replacing with two steps each of steps 26, 28, 51, 53, 56, 65, 85, 87, 90, 110, 113, 114, 140, 143, 145, 165, 173, 178, 189):




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