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A 6x6 checkerboard is tiled arbitrarily with eighteen 1x2 dominoes. A new square is added to the right-hand side of the board, making the top row length 7. At any time you may move a domino from i...
#1: Initial revision
by
will.octagon.gibson
·
2026-03-14T06:38:26Z (6 months ago)
Can you make all the dominoes horizontal?
A 6x6 checkerboard is tiled arbitrarily with eighteen 1x2 dominoes. A new square is added to the right-hand side of the board, making the top row length 7. At any time you may move a domino from its current position to a new one, provided that after the domino is lifted, there are two adjacent empty squares to receive it. Can you retile the augmented checkerboard so that all the dominoes are horizontal no matter how the checkerboard was initially tiled? If you wish, you can experiment with moving dominoes [here.](https://openprocessing.org/sketch/2855040) --- Attribution: This puzzle is a slight variant of a puzzle from: ***Mathematical Puzzles*** by Peter Winkler