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Mathematics 18 Online
OpenStudy (anonymous):

Use mathematical induction to show that a rectangular checkerboard with an even number of cells and two squares missing, one white and one black, can be covered by dominoes.

OpenStudy (asnaseer):

I assume the cells that are removed MUST be adjacent to one another - otherwise there is no proof as you can find lots of examples where you can randomly remove one white cell and one black square to leave a board that cannot be covered by dominoes. so, with this assumption: 1. a rectangular checkerboard with an even number of cells can always be covered by dominoes. 2. adjacent cells along a diagonal are always of the same colour. so to remove one white and one black cell, you MUST remove cells that are side-by-side (vertically or horizontally). this means that the two cells you remove resemble a domino piece which means what remains can still be covered by dominoes as the entire original board could have been covered by dominoes and you have effectively just removed one domino piece

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