Cut out in cardboard twenty triangular pieces exactly the size and shape of this one, and try to place them together so that they form a perfect square.
ANOTHER MYSTIC NUMBER
The decimal equivalent of 1⁄13 is .076923. This (omitting the point), multiplied by 1, 3, 4, 9, 10, or 12, yields results in which the same figures appear in varied order, but similar sequence, and multiplied by 2, 5, 6, 7, 8, or 11, it yields a different series, with similar characteristics. Thus:—
| 76923 | × | 1 | = | 76923 | 76923 | × | 2 | = | 153846 |
| × | 3 | = | 230769 | × | 5 | = | 384615 | ||
| × | 4 | = | 307692 | × | 6 | = | 461538 | ||
| × | 9 | = | 692307 | × | 7 | = | 538461 | ||
| × | 10 | = | 769230 | × | 8 | = | 615384 | ||
| × | 12 | = | 923076 | × | 11 | = | 846153 |
DON’T BUY IT TO TRY IT
A kaleidoscope cylinder contains twenty small pieces of coloured glass. As we turn it round, or shake it, so as to make ten changes of pattern every minute, it will take the inconceivable space of time of 462,880,899,576 years and 360 days to exhaust all the possible symmetrical variations. (The 360 days is good!)
No. LXXXI.—PINS AND DOTS
Here is an amusing little exercise for the ingenuity of our solvers.