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Since the square is known to be magic, we can assume from basic "magic theory" that the missing numbers are those absent at the moment from the series 1 to 16. The main insight then required is to spot that the third column from the left must contain both 2 and 3, in order to achieve the 34 constant (because 1 and 4 are already positioned).
Next, examination of the possibilities for the 15, ?, ?, 12 diagonal reveals that the 2 will need to be next to the 12, thus making the complete diagonal 15, 5, 2, 12. The rest is easy.
Ivor Smith will receive £20 for this neat little contribution.
Here is the completed array:
| 1 | 8 | 13 | 12 |
|---|---|---|---|
| 14 |
11 |
2 |
7 |
| 4 |
5 |
16 |
9 |
| 15 |
10 |
3 |
6 |
14 Jun 2009