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