Luke McShane

A multitude of queens

issue 22 January 2022

Here’s a challenge which appeared in a German chess magazine in 1848: place eight white queens on an empty chessboard so that no two queens occupy the same file, rank or diagonal. In other words, none of the queens may defend each other.

Perhaps you start with a queen in the top left corner, on a8. The next might be placed on the adjacent file, nearby but not touching, on the b6 square, a knight’s move away from the first. Following the pattern, you put another on c4, and a fourth one on d2. For the e-file, we need to break the pattern, so let’s revert to near the top of the board, on e7. Flushed with success, you see that the ‘knight move’ pattern still works, and plonk two more queens on f5 and g3. Giddily, you add the last queen on h1, the only unused file and rank, and — bloody hell! — it conflicts with the first queen you placed on a8.

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