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# Challenge question

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How many ways can a domino be placed on a chessboard? Each "half" of the domino must cover exactly one square of the chessboard.

Guest Apr 30, 2018
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Sorry, my previous answer was wrong.

Corner dominoes have two options, but regular squares have 3 or even 4.

Here is the correct one.

If the domino is oriented horizontally,

its position is determined by the leftmost square it covers,

for which there are $$7\cdot8=56$$

possibilities (the rightmost file is excluded).

Similar for vertical orientation. Thus, there are $$2\cdot56=112$$ possibilities in total.

I hope this helped,

Gavin.

GYanggg  Apr 30, 2018
edited by GYanggg  Apr 30, 2018