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Brainteasers

Can a knight tour a 3 by 3 board?

chessboardknights-tourgraphsimpossibility
  1. Can a knight visit every square of a 3 by 3 board exactly once, starting anywhere?
  2. Can it do so on a 3 by 4 board?
  3. What is the smallest board on which a knight's tour exists, and why do boards one or two squares wide never have one?
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On a 3 by 3 board, which squares can a knight move to from the centre?

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Graph Traversal, BFS and DFSGraph Theory BasicsAdaptive Versus Pre-Committed Weighing StrategiesThe Lost Boarding Pass ProblemAM-GM as a Puzzle Tool

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