Another unique example is the following:
| 3 | 20 | 7 | 24 | 11 |
| 16 | 8 | 25 | 12 | 4 |
| 9 | 21 | 13 | 5 | 17 |
| 22 | 14 | 1 | 18 | 10 |
| 15 | 2 | 19 | 6 | 23 |
In this case the sum is 65, and can be reached in an almost endless variety of combinations. However, there is one feature to be remembered in dealing with this problem, and that is that the central number (13) must be added to each combination except in the straight and diagonal lines. Thus: 20, 24, 2, 6, and 13, or 8, 12, 14, 18, and 13, etc., each make the magic sum 65.
The well-known “15 puzzle” is another illustration of the surprising feats which figures are sometimes made to play. The problem being to arrange in a square of three rows, three figures in each row, the numerals, 1 to 9 inclusive, in such a manner that each row—vertical, horizontal, or diagonal—will total 15. This is more difficult than appears at first glance, unless you have the key, which is: place 5 in the center, and let the four corners be 2, 4, 6, and 8. The rest is easy.
| 2 | 9 | 4 |
| 7 | 5 | 3 |
| 6 | 1 | 8 |
This form differs from the 65 and 34 in that it can only be added diagonally, horizontally, and vertically.
TRANSCRIBER’S NOTES
- Silently corrected obvious typographical errors and variations in spelling.
- Retained archaic, non-standard, and uncertain spellings as printed.