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Anti-magic Square

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

A 4 by 4 "anti-magic square" is an arrangement of the numbers 1 to 16 inclusive in a square, so that the totals of each of the four rows and four columns and two main diagonals are ten consecutive numbers in some order. The diagram shows an incomplete magic square. Can you complete it?

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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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