Magic Knight's Tours in Higher Dimensions

A knight‟s tour on a board is a sequence of knight moves that visits each square exactly once. A knight‟s tour on a square board is called magic knight‟s tour if the sum of the numbers in each row and column is the same (magic constant). Knight‟s tour in higher dimensions (n > 3) is a new topic in the age-old world of knight‟s tours. In this paper, it has been proved that there can‟t be magic knight‟s tour or closed knight‟s tour in an odd order n-dimensional hypercube. 3 x 4 x 2 n-2 is the smallest cuboid (n ≥ 2) and 4 x 4 x 4 n-2 is the smallest cube in which knight‟s tour is possible in n-dimensions (n ≥ 3). Magic knight‟s tours are possible in 4 x 4 x 4 x 4 and 4 x 4 x 4 x 4 x 4 hypercube.