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These solution counts are total counts for each basic shape that can be done in a checkered pattern. Several other parallelepiped shapes are possible but cannot be solved in this manner. What is important about providing this list with the puzzle is that it offers a good indication of the degree of difficulty associated with each shape. To determine solution counts, I programmed an Apple II to find all solutions to all possible shapes. Needless to say, with only 48K of RAM and a 6502, 1 MHz CPU, it took a very long time ... See More: Puzzle Details Puzzle History Versions Produced Solutions List Solution Examples |
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My initial computer program found 1,111 total solutions for levels 1-6 (those flat shapes) and the levels 7-13 the total solutions were 3,333 which, mathematically made sense - 4,444. But my definitions of 'mirror image' and 'rotation' duplication were not held true by the puzzle community. This was pointed out to me when Jacques Haubrich, co-author of 'Compendium of Checkerboard Puzzles', ran my puzzle through his computer - A RISC-OS running on an ARM processor. He did in minutes what took weeks on my old system. Basically our computer programs agreed on the 1,111 flat
solutions but the counts for the 3 dimensional shapes were not
similar due to different formulas used in 3D. The definitions by
the puzzle community were a good standard to go on and the above
list is based on that standard. |
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