Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?

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The Electronic Journal of Combinatorics, Vol: 18

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DeMaio, Joseph; Bindia, Mathew
chess; games; Applied Mathematics; Mathematics
article description
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the m x n rectangular chessboards that admit a closed knight's tour. In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying the i x j x k rectangular prisms that admit a closed knight's tour.