Solution #12: Dominoes on Board
The use of a chessman to block out the middle square gives the clue to the
solution of this problem. If the board is marked out as a chess board with
alternate black and white squares, with the middle square black, we find that
there are 32 white squares and 30 black squares (not counting the middle
square). Now a domino however placed will cover one white square and one black
square and hence having placed 30 dominoes we shall always be left with 2 white
squares which cannot possibly be covered by a single domino.
Hence, there is no possible solution to the problem.
Source: Longley-Cook, L. H.
Categories: Reasoning, Favorite