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Longest uncrossed knight's path
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Longest uncrossed knight's path : ウィキペディア英語版
Longest uncrossed knight's path
The longest uncrossed (or nonintersecting) knight's path is a mathematical problem involving a knight on the standard 8×8 chessboard or, more generally, on a square ''n''×''n'' board. The problem is to find the longest path the knight can take on the given board, such that the path does not intersect itself. A further distinction can be made between a closed path, which ends on the same field as where it begins, and an open path, which ends on a different field from where it begins.
== Known solutions ==
The longest open paths are known only for ''n'' ≤ 9. Their lengths for ''n'' = 1, 2, …, 9 are:
:0, 0, 2, 5, 10, 17, 24, 35, 47
The longest closed paths are known only for ''n'' ≤ 10. Their lengths for ''n'' = 1, 2, …, 10 are:
: 0, 0, 0, 4, 8, 12, 24, 32, 42, 54

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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