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tician. The property to which I allude is this, that when 9 is multiplied by 2, by 3, by 4, by 5, by 6, &c., it will be found that the digits composing the product, when added together, give 9. Thus:
| 2 × 9 = 18, | and | 1 + 8 = 9 |
| 3 × 9 = 27 | ,, | 2 + 7 = 9 |
| 4 × 9 = 36 | ,, | 3 + 6 = 9 |
| 5 × 9 = 45 | ,, | 4 + 5 = 9 |
| 6 × 9 = 54 | ,, | 5 + 4 = 9 |
| 7 × 9 = 63 | ,, | 6 + 3 = 9 |
| 8 × 9 = 72 | ,, | 7 + 2 = 9 |
| 9 × 9 = 81 | ,, | 8 + 1 = 9 |
| 10 × 9 = 90 | ,, | 9 + 0 = 9 |
It will be noticed that 9 × 11 makes 99, the sum of the digits of which is 18 and not 9, but the sum of the digits 1 + 8 equals 9.
| 9 × 12 = 108, | and | 1 + 0 + 8 = 9 |
| 9 × 13 = 117 | ,, | 1 + 1 + 7 = 9 |
| 9 × 14 = 126 | ,, | 1 + 2 + 6 = 9 |
And so on to any extent.
M. de Maivan discovered another singular property of the same number. If the order of the digits expressing a number be changed, and this number be subtracted from the former, the remainder will be 9 or a multiple of 9, and, being a multiple, the sum of its digits will be 9.
For instance, take the number 21, reverse the digits, and you have 12; subtract 12 from 21, and
