A Knight

1
A Knights Tour

• A decision problem

2
A Legal Move

• Can only move 1 x 2
• ...Or 2 x 1

3
A Knights 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
Magic Knights Tour

• Some tours can be semi-magic
• An example of a semi-magic tour
• There are no fully magic tours

7
Different Chess Boards
8
The Knights Graph

• Related to the knights problem

9
Graphs of Other Pieces
Rooks Graph
Kings Graph
10
How Can the Problem be Further Explored?

• By investigating variations on the knights move

11
Explore the Problem for Yourself

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