The Journey Of The King

Probability Level 3

Two squares on an 8 × 8 8\times8 chessboard are called touching if they have at least one common vertex. Determine if it is possible for a king to begin in some square and visit all the squares exactly once in such a way that all moves except the first are made into squares touching an even number of squares already visited.

It's always possible It isn't possible It's impossible if and only if he starts on the corners It's impossible if and only if he starts on the edges

Mateo Matijasevick by Mateo Matijasevick , 22, Colombia

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1 solution

Mark Hennings
Apr 6, 2016

See this reference . It is a simple parity argument that tours of this type are not possible on nontrivial m × n m \times n boards if m m and n n have the same parity. Tours are not possible on other sized boards (except 1 × 1 1 \times 1 or 1 × 2 1 \times 2 ones), but the proof is harder.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Has not to be proved! Simple trial-and-error shows the evidence very quickly.

Andreas Wendler - 5 years, 2 months ago

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