SOLUTIONS
No. V.—THE MAKING OF A MAGIC SQUARE
The perfect Magic Square, for which we have given the construction of two preparatory squares, is formed by placing one of these over the other, so that the numbers in their corresponding cells combine, as is shown below.
Preparatory Square No. 1.
| * | ||||
| 1 | 3 | 5 | 2 | 4 |
| 5 | 2 | 4 | 1 | 3 |
| 4 | 1 | 3 | 5 | 2 |
| 3 | 5 | 2 | 4 | 1 |
| 2 | 4 | 1 | 3 | 5 |
Preparatory Square No. 2.
| * | ||||
| 5 | 15 | 0 | 10 | 20 |
| 10 | 20 | 5 | 15 | 0 |
| 15 | 0 | 10 | 20 | 5 |
| 20 | 5 | 15 | 0 | 10 |
| 0 | 10 | 20 | 5 | 15 |
The Perfect Magic Square.
| 6 | 18 | 5 | 12 | 24 |
| 15 | 22 | 9 | 16 | 3 |
| 19 | 1 | 13 | 25 | 7 |
| 23 | 10 | 17 | 4 | 11 |
| 2 | 14 | 21 | 8 | 20 |
No less than 57,600 Magic Squares can be formed with twenty-five cells by varying the arrangement of these same figures, but not many are so perfect as our specimen, in which sixty-five can be counted in forty-two ways. These comprise each horizontal row; each perpendicular row; main diagonals; blended diagonals from every corner (such as 6, with 14, 17, 25, 3; or 15, 18, with 21, 4, 7); centre with any four equidistant in outer cells; any perfect St George’s cross (such as 18, 22, 1, 15, 9); and any perfect St Andrew’s cross (such as 6, 22, 13, 5, 19).