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## 'Knight Defeated' printed from http://nrich.maths.org/

You do not need to be able to play chess to solve this
problem.

The standard move for a knight on a chess board is $2$ steps in one
direction and one step in the other direction. A knight's tour is a
sequence of moves in which the knight visits every square on the
board once and only once and a circuit is a tour in which the
knight returns to the starting point.

Prove that a knight cannot make a tour on a $2$ by $n$ board for
any value of $n$.

How many different tours can you find on a $3$ by $4$ rectangular
board?

Prove that a knight cannot make a circuit on a $3$ by $4$
rectangular board.