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The Knight's Tour in 3-Dimensional Chess
by John R Gerlach, Navitas Data Sciences and Scott M Gerlach, Dartmouth College
Three dimensional chess uses two or more chess boards such that a chess piece can traverse the several boards according to the rules for that piece. Thus, the knight can remain on the board where it resides or moves one or two steps to a successive board, then move its remaining steps. In three-dimensional chess, the Knight's Tour is a sequence of moves on multiple 8x8 chess boards such that a knight visits each square only once. Thus, for three boards, there would be 192 squares visited only once.
The paper, The Knight's Tour in Chess - Implementing a Heuristic Solution (Gerlach 2015), explains a SAS® solution for finding the knight's tour on a single board, starting from any square on the board. This paper discusses several scenarios and solutions for generating the knight's tour in three-dimensional chess.