Solution: 34 is the key to the magic square

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).

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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 13   12

14

11

2

7

4

5

16

9

15

10

3

6