| 987654321 | = | 45. |
| 123456789 | = | 45. |
| 864197532 | = | 45. |
No. LXXVIII.—THE BROKEN OCTAGON
Cut out in stiff cardboard four pieces shaped as Fig. 1, four as Fig. 2, and four as Fig. 3, taking care that they are all exactly true to pattern in shape and proportion to one another.
Now see whether you can put the twelve pieces together so as to form a perfect octagon.
PROPERTIES OF SEVEN
Here is a proof that 7, if it cannot rival the mystic 9, has quaint properties of its own:—
| 1 | 5 | 8 | 7 | 3 | × | 7 | = | 1 | 1 | 1 | 1 | 1 | 1 | |
| 3 | 1 | 7 | 4 | 6 | × | 7 | = | 2 | 2 | 2 | 2 | 2 | 2 | |
| 4 | 7 | 6 | 1 | 9 | × | 7 | = | 3 | 3 | 3 | 3 | 3 | 3 | |
| 6 | 3 | 4 | 9 | 2 | × | 7 | = | 4 | 4 | 4 | 4 | 4 | 4 | |
| 7 | 9 | 3 | 6 | 5 | × | 7 | = | 5 | 5 | 5 | 5 | 5 | 5 | |
| 9 | 5 | 2 | 3 | 8 | × | 7 | = | 6 | 6 | 6 | 6 | 6 | 6 | |
| 1 | 1 | 1 | 1 | 1 | 1 | × | 7 | = | 7 | 7 | 7 | 7 | 7 | 7 |
| 1 | 2 | 6 | 9 | 8 | 4 | × | 7 | = | 8 | 8 | 8 | 8 | 8 | 8 |
| 1 | 4 | 2 | 8 | 5 | 7 | × | 7 | = | 9 | 9 | 9 | 9 | 9 | 9 |