Challenge Level

A 4 by 4 "anti-magic square" is an arrangement of the numbers 1 to 16 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 anti-magic square.

4 | 5 | 7 | 14 |

6 | 13 | 3 | |

11 | 12 | 9 | |

10 |

Can you fill in the missing numbers (1, 2, 8, 15 and 16) to 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.

You can find more short problems, arranged by curriculum topic, in our short problems collection.