5.F.3. KNIGHT'S TOURS IN HIGHER DIMENSIONS
A. T. Vandermonde. Remarques sur les problèmes de situation. Hist. de l'Acad. des Sci. avec les Mémoires (Paris) (1771 (1774)) Mémoires: pp. 566 574 & Plates I & II. ??NYS. First? mention of cubical problem. (Not given in BLW excerpt.)
F. Maack. Mitt. über Raumschak. 1909, No. 2, p. 31. ??NYS -- cited by Gibbins, below. Knight's tour on 4 x 4 x 4 board.
Dudeney. AM. 1917. Prob. 340: The cubic knight's tour, pp. 103 & 229. Says Vandermonde asked for a tour on the faces of a 8 x 8 x 8 cube. He gives it as a problem with a solution.
N. M. Gibbins. Chess in three and four dimensions. MG 28 (No. 279) (1944) 46 50. Gives knight's tour on 3 x 3 x 4 board -- an unpublished result due to E. Hubar Stockar of Geneva. This is the smallest 3 D board with a tour. Gives Maack's tour on 4 x 4 x 4 board.
Ian Stewart. Solid knight's tours. JRM 4:1 (Jan 1971) 1. Cites Dudeney. Gives a tour through the entire 8 x 8 x 8 cube by stacking 8 knight's paths.
T. W. Marlow. Closed knight tour of a 4 x 4 x 4 board. Chessics 29 & 30 (1987) 162. Inspired by Stewart.
Dostları ilə paylaş: | 
