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The $n$-queens problem in higher dimensions. (English)
Elem. Math. 61, No. 4, 133-137 (2006).
The paper considers the $d$-dimensional chessboard, where the fields are $(q_1,q_2,\dots,q_d)$ with $q_i\in\{0,1,\dots,d-1\}$. The attack lines of a queen placed at $(q_1,q_2,\dots,q_d)$ are described as solutions to the system of equations $\pm(x_1-q_1)=\pm(x_2-q_2)=\dots=\pm(x_d-q_d)$ with a any fixed choices of signes, i.e. there are $2^{d-1}$ different sets of equations. Later Lemma 2.1 gives a different description to the attack lines of a queen, according to which lines defined by a vector whose every coordinate is $0$ or $\pm 1$ are the attack lines. Some elementary facts are observed.
Reviewer: László A. Székely (Columbia)
Keywords: $n$-queens problem