1. A Knight’s Tour A decision problem

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

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

4. 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

5. One Possible Solution

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

7. Different Chess Boards

8. The Knight’s Graph Related to the knights problem

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

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

11. 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