It is interesting to note that the repeated addition of odd numbers to one another can be so arranged as to produce cube numbers in due sequence. Thus:—
| 1 | = | 1 × 1 × 1 |
| 3 + 5 | = | 2 × 2 × 2 |
| 7 + 9 + 11 | = | 3 × 3 × 3 |
| 13 + 15 + 17 + 19 | = | 4 × 4 × 4 |
| 21 + 23 + 25 + 27 + 29 | = | 5 × 5 × 5 |
and so on, to any extent.
No. LXXVI.—ROUND THE GARDEN
In a large old-fashioned garden walks were arranged round a central fountain in the shape of a Maltese cross.
If four persons started at noon from the fountain, walking round the four paths at two, three, four and five miles an hour respectively, at what time would they meet for the third time at their starting-point, if the distance on each track was one-third of a mile?
A NICE SHORT CUT
When the tens of two numbers are the same, and their units added together make ten, multiply the units together, increase one of the tens by unity, and multiply it by the other ten. The result is the product of the two original numbers, if the first result follows the other. Thus:—