No. XXXI.—MAGIC TRIANGLES
The subjoined diagram shows the order in which the first 18 numbers can be arranged so that they count 19, 38, or 57 in many ways, down, across, or along some angles, 19 in 6 ways, 38 in 12, and 57 in 14 ways.
Thus, for examples—
| 7 | + | 12 | = | 14 | + | 5 | = | 4 | + | 15 | = | 19 |
| 7 | + | 11 | + | 14 | + | 6 | ——— | = | 38 | |||
| 7 | + | 14 | + | 4 | + | 5 | + | 12 | + | 15 | = | 57 |
No. XXXIV.—MAGIC HEXAGON IN A CIRCLE
The figures in the Magic Hexagon must be arranged as is shown in this diagram:—
