A Knight’s Tour A decision problem. A Legal Move Can only move 1 x 2...Or 2 x 1.

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A Knight’s Tour A decision problem

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

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

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

One Possible Solution

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

Different Chess Boards

The Knight’s Graph Related to the knights problem

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

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

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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