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

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,



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

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