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Problem of the Week 1161
Consider a 4×100 chessboard. Show that there is an open knight's tour (also called a Hamiltonian path) from some white square to some black square. That is, find a sequence of knight's moves that lands on each square exactly once.
If you solve this case, you will no doubt have solved the general
Note that there is no Hamiltonian cycle for knights on a
As I was working on the problem, I asked it of John Watkins (Colorado College), and within a short time he found (by hand I believe) the solution for the full 4-case as well.
© Copyright 2012 Stan Wagon. Reproduced with permission.
4 December 2012