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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. 

 

 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.

 Apr 30, 2018
edited by GYanggg  Apr 30, 2018

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