On an 8x8 chess board you remove two opposite corners.
Can the rest of the board be exactly covered with 1x2 dominoes, without overlapping or leaving gaps?
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Mutilated board and dominoes
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- Since each domino covers one of each color, a complete coverage would require equality of colors, which is not met here.
- On a normal 8x8 board there are 32 white and 32 black. If you remove two opposite corners (same color), there are 30 of one color and 32 of the other.
- Final section: On a normal 8x8 board there are 32 white and 32 black. If you remove two opposite corners (same color), there are 30 of one color and 32 of the other. Then, since each domino covers one of each color, a complete coverage would require equality of colors, which is not fulfilled here.
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Answer: It is not possible.
A domino always covers 1 white and 1 black square.
On a normal 8x8 board there are 32 white and 32 black. If you remove two opposite corners (same color), there are 30 of one color and 32 of the other.
Since each domino covers one of each color, a complete coverage would require equality of colors, which is not met here.
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