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This is the sort of problem that needs a lot of thinking time.
Present it and leave it for a week or so before returning to it ...
If no one has made much progress - what have they managed to do?
At some stage it may be worth mentioning that the solution requires more than 20 moves.
What recording methods have people come up with?
Then the big question:
How can you know you have managed to swap the knights in the minimum number of moves? This will certainly need a convincing recording system.
Knights Moving
Age 16 to 18
Challenge Level 
This is the sort of problem that needs a lot of thinking time.
Present it and leave it for a week or so before returning to it ...
If no one has made much progress - what have they managed to do?
At some stage it may be worth mentioning that the solution requires more than 20 moves.
What recording methods have people come up with?
Then the big question:
How can you know you have managed to swap the knights in the minimum number of moves? This will certainly need a convincing recording system.
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A Knight's Journey
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
