No: XXIV.—MAGIC FRACTIONS
Here is an arrangement of fractions which form a perfect Magic Square:—
| 38 | 512 | 524 |
| 16 | 13 | 12 |
| 1124 | 14 | 724 |
If these fractions are added together in any one of the eight directions, the result in every case is unity. Thus 3⁄8 + 1⁄3 + 7⁄24 = 1, 1⁄6 + 1⁄3 + 1⁄2 = 1, and so on throughout the rows, columns, and diagonals.
14
“DOUBLE, DOUBLE, TOIL AND TROUBLE!”
“By hammer and hand
All arts do stand”—
So says an ancient saw;
But hammer and hand
Will work or stand
By my unwritten law.
Behold me, as sparks from the anvils fly,
But fires lie down at my bitter cry.
No. XXV.—MORE MAGIC FRACTIONS
We are indebted to a friend for the following elaborate Magic Square of fractions, on the lines of that on the preceding page.
| 1980 | 720 | 140 | 1180 | 14 |
| 1340 | 18 | 980 | 940 | 1780 |
| 110 | 780 | 15 | 516 | 310 |
| 316 | 740 | 2380 | 1140 | 340 |
| 320 | 2180 | 38 | 120 | 1380 |