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The chessboard has rotational symmetry: if you turn it 180 degrees it is the same. Would not all tours be invariant under 180 degree rotation? EDIT: Sorry, I u
by mhansen 17y ago
The chessboard has rotational symmetry: if you turn it 180 degrees it is the same. Would not all tours be invariant under 180 degree rotation?
EDIT: Sorry, I understand now. If the knight's tour ends directly opposite it's starting position, it is invariant under 180 degree rotation.
- randomwalker 17y agoThis might help: http://www.mathpuzzle.com/leapers.htm http://www.mathpuzzle.com/leapers.htm As you can see from those examples, a symmetric tour is a rather regular-looking object; a random tour has an extremely low probability of being symmetric.
- mhansen 17y agoAh, thank you!