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Why do this problem?

This problem is presented for the more able pupils and can challenge them both in number and spatial skills. 

Possible approach

The six by six grid can be printed from here ( doc. pdf ), and then presented to the pupil. The challenge may need to be explained very clearly so as to prevent a lot of unnecessary calculations being made. 

Key questions

How did you arrive at this? Explain to me the solutions that you have come to.