The multilated chessboard

Logic Level 2

In $1961$ , the British theoretical physicist M.E.Fisher solved famous and very tough problem. He showed that an $8*8$ chess board can be covered by $2*1$ dominoes in $2^4$ * $901^2$ or $12988816$ ways. Now let us cut out two diagonally opposite corners of the board. In how many ways can u cover the $62$ squares of the multilated chess board with $31$ dominoes?

31 Can't be covered 30 33 32

1 solution

Adarsh Adi
Feb 12, 2018

The problem is trivial. Indeed ,each domino covers one black and one white square. If a covering of chessboard existed ,it would cover $31$ black and $31$ white squares. But the multilated chessboard has $30$ squares of one colour and $32$ squares of the other colour.

The multilated chessboard

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