Any series of numbers that can be divided by 9, as 365, 472,821,754, &c., being shown, a person may be requested to multiply secretly either of these series by any figure he pleases, to strike out one number of the quotient, and to let you know the figures which remain, in any order he likes; you will then, by the assistance of the knowledge of the above properties of 9, easily declare the number which has been erased. Thus, suppose 365,472 are the numbers chosen, and the multiplier is six; if then, 8 is stuck out, the numbers returned to you will be
| } | 2 | |
| } | 1 | |
| 365472 | } | 9 |
| 6 | } | 2 |
| ——— | } | 3 |
| 219232 | } | 2 |
| } | — | |
| } | 19 |
The amount of these numbers is 19; but 19, divided by 9, leaves a remainder of 1; you, therefore, want 8 to complete another 9: 8, then, is the number erased.
The component figures of the product made by the multiplication of every digit into the number 9, when added together, make NINE.
The order of these component figures is reversed after the said number has been multiplied by 5.
The component figures of the amount of the multipliers (viz. 45,) when added together, make NINE.
The amount by the several products, or multiples of 9 (viz. 405,) when divided by 9, gives for a quotient, 45; that is, 4 + 5 = NINE.
The amount of the first product (viz. 9,) when added to the other product, whose respective component figures make 9, is 81; which is the square of NINE.
The said number 81, when added to the above mentioned amount of the several products, or multiples of 9 (viz. 405) makes 486, which, if divided by 9, gives for a quotient 54: that is, 5 + 4 = NINE.