Non-crossing Knight's Tour in 3-Dimension

Details Non-crossing Knight's Tour in 3-Dimension Non-crossing Knight's Tour in 3-Dimension

2008-03-29

arxiv.org/abs/0803.4259v1

Mathematics

Combinatorics

6 pages, 13 figures

Scientific paper

Non-crossing knight's tours in 3-dimension is a new field of research. The author has shown its possibility in small cuboids and in cubes up to 8x8x8 size. It can also be extended to larger size cubes and cuboids. The author has achieved jumps of length 15, 46, 88, 159, 258 and 395 in cubes of size 3x3x3, 4x4x4, 5x5x5, 6x6x6, 7x7x7 and 8x8x8 respectively. This amounts to covering 59%, 73%, 71%, 74%, 76% and 77% cells in these cubes.

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