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arXiv · 1907.09120

Queens in exile: non-attacking queens on infinite chess boards

F. Michel Dekking·Jeffrey Shallit·N. J. A. Sloane
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Abstract

Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, ... Consider the cells in order, placing a queen in a cell if and only if it would not attack any earlier queen. The problem is to determine the positions of the queens. We study the problem for a doubly-infinite chessboard of size Z x Z numbered along a square spiral, and an infinite single-quadrant chessboard (of size N x N) numbered along antidiagonals. We give a fairly complete solution in the first case, based on the Tribonacci word. There are connections with combinatorial games.

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F. Michel Dekking, Jeffrey Shallit, N. J. A. Sloane. 2019-07-28. Queens in exile: non-attacking queens on infinite chess boards. https://arxiv.org/abs/1907.09120

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