$Is\quad it\quad possible?$

Probability Level 2

Suppose a standard $8*8$ chessboard has two diagonally opposite corners removed, leaving $62$ squares. Is it possible to place $31$ dominoes of size $2*1$ so as to cover all of these squares?

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1 solution

Otto Bretscher
May 4, 2015

The squares we remove in opposite corners have the same color; let's say they are both black. Then there are only 30 black squares left, meaning that we can place at most 30 dominoes, since every domino will cover a white as well as a black square.

@Otto Bretscher Sir, here .....

Aaghaz Mahajan - 2 years, 2 months ago

I s i t p o s s i b l e ? Is\quad it\quad possible? I s i t p o s s i b l e ?

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$Is\quad it\quad possible?$