Impossible Dominos' Arrangement on Chessboard
What was the challenge given?
Initial mathematical calculations might suggest that the task is pretty simple. If 2 square are cut off from 64 squares then 62 squares will be left which are enough for 31 dominos (each covering 2 squares).
But, that is not the case. Since, 2 diagonally opposite squares are removed, they has to be either black or white like shown below with shaded regions.
We need 1 black and 1 White square for placement of 1 domino on the chessboard.That is 31 Black and 31 White squares are needed to give cover for 31 dominos.
In the above 2 cases, there are either 32 Black and 30 White or 30 Black and 32 White squares are available.
This makes the task of placing 31 dominos on the chessboard (whose 2 diagonally opposite squares are removed) impossible!
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