This square is a good example by which to illustrate one of the methods of construction of these interesting devices. Thus, place 1 in the middle square of the top row, and then write the numbers down consecutively, always working in the direction of the arrows as indicated. When any number falls outside, as number 2 does at the start, drop down to the extreme square in the next row and insert the number there, as was done in this case. It will be observed that 4 falls outside, and so it is moved to the proper square as suggested, which will be at the extreme left of the next row above. Continuing, it is found that at 6 it is necessary to drop down one square and continue in the direction of the arrows. At 9 it is necessary to drop down to the proper extreme square as shown. The next number, 10, must again be provided for at the square on the left of the next higher row. The square ahead being already filled, 11 is placed below; after this there is “clear sailing” for a time. In this manner magic squares with seven or nine numbers to the side may be made easily. When puzzles and catch problems are under discussion, it is always mystifying to take one’s pencil and quickly make out a magic square according to this easily remembered method. The small diagrams at D suggest some of the combinations.
Another method of constructing a square of 25 numbers diagonally is shown at [E]. Place the outside numbers in the open spaces at the opposite side of the square, maintaining the same triangular relation, which results in the arrangement shown at [F]. While this combination is entirely different from the previous one, it exhibits the same mysterious properties.
| 15 | 10 | 3 | 6 |
| 4 | 5 | 16 | 9 |
| 14 | 11 | 2 | 7 |
| 1 | 8 | 13 | 12 |
A
| 1 | 15 | 14 | 4 |
| 12 | 6 | 7 | 9 |
| 8 | 10 | 11 | 5 |
| 13 | 3 | 2 | 16 |
B
| 9 | 7 | 14 | 4 |
| 6 | 12 | 1 | 15 |
| 3 | 13 | 8 | 10 |
| 16 | 2 | 11 | 5 |
C
| 17 | 24 | 1 | 8 | 15 |
| 23 | 5 | 7 | 14 | 16 |
| 4 | 6 | 13 | 20 | 22 |
| 10 | 12 | 19 | 21 | 3 |
| 11 | 18 | 25 | 2 | 9 |