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A Knight’s Tour A decision problem

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A Legal Move Can only move 1 x 2...Or 2 x 1

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A Knight’s Tour In this problem:...Every single square, once only!

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Solving The Tour Similar problems were studied 4000 years ago Modern chess variety studied by various mathematicians Today, computers can use backtracking to find solutions

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One Possible Solution

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Some tours can be semi-magic An example of a semi-magic tour There are no fully magic tours Magic Knight’s Tour

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Different Chess Boards

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The Knight’s Graph Related to the knights problem

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Graphs of Other Pieces King’s Graph Rook’s Graph

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How Can the Problem be Further Explored? By investigating variations on the knight’s move

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Explore the Problem for Yourself Try to solve the knight's tour Detailed diagrams of the tour, with numbered movements Detailed diagrams of the tour, with numbered movements Pre - chess pieces and magic squares Detailed introduction with backtracking demonstration Detailed introduction with backtracking demonstration

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Welcome to Chess Class This will program will show you basic Chess moves Copyright William J Capehart.

Welcome to Chess Class This will program will show you basic Chess moves Copyright William J Capehart.

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