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Published on 2018. március 08. csütörtök, 08:30

The man is overtaken by his fate .... :-)

As a soldier in 1981 I survived the boring periods by trying to walk around every square of a chess board by a knight. Returning to the university, in the first summer, in 1982, this boredom reliever problem came up again and I started to find the size of all the chess boards that can be walked or walked around by a knight. This short thinking filled the pages of a checkered booklet, which I found, scanned and placed on my website in 2010 at a tidying up. It can still be downloaded. There is complete proof in the booklet for the next theorem.

Theorem

• Each rectangular chess board that contains a 4*4 square is walkable by knight (that is, it has a Hamiltonian path).
• A rectangular chess board can be walked around by knight (so it has a Hamiltonian circle) if and only if it contains a 5*5 square and one of its sides is even.

This little entertaining "work" appeared last week (March 2nd) in my daughter's high school and, moreover, in her class as a good example for the Hamilton path and circle of a graph.