(related to Problem: Bishops in Convocation)

The fourteen bishops may be placed in $256$ different ways. But every bishop must always be placed on one of the sides of the board — that is, somewhere on a row or file on the extreme edge. The puzzle, therefore, consists in counting the number of different ways that we can arrange the fourteen around the edge of the board without attack. This is not a difficult matter. On a chessboard of $n^2$ squares $2n- 2$ bishops (the maximum number) may always be placed in $2^n$ ways without attacking. On an ordinary chessboard $n$ would be $8;$, therefore, $14$ bishops may be placed in $256$ different ways. It is rather curious that the general result should come out in so simple a form.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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