HOW A NUMBER THOUGHT OF OR OTHERWISE INDICATED MAY BE TOLD.
These rules and puzzles are numerous, and in practising them in company it is well to have several methods at command, in order that those of the company not in the secret may be the more mystified; and, indeed, those who only know one or two ways will themselves be astonished if they see others proceeding on principles differing from those with which they are familiar.
The Cancelled Figure.—Write down on a slate a series of numbers, the sum of each of which shall be 9: such, for example, as 18, 27, 36, 45, 144, 234, 612, 711, 252, 342, 261, 360, 432, 315, &c. &c. The greater the variety the better. Tell some person to fix on two of these numbers, and after adding them together, to strike out any one of the figures of the result, and then, upon his stating the sum of the remaining figure or figures, the figure struck out may be arrived at by ascertaining the difference between that sum and 9 or 18, according to whether the sum is less or more than 9. If the sum remaining be 9, the figure struck out will have been 9. Suppose, for instance, the numbers selected are 711 and 252, the total of which will be 963; if the figure struck out of that number be 6, the sum of the two remaining figures will be 12, or 6 less than 18. Again, take the numbers 18 and 27, making a total of 45; strike out the 5, and it will be seen that the difference between 4 and 9 is 5.
In the following methods any number may be thought of, and the subsequent calculations are to be mentally or otherwise made by him thinking of the number.
First Method.—Instruct that the number thought of be multiplied by 3, that 1 be added to the result, the result again being multiplied by 3, to which result the number first thought of has to be added; ask the result, strike off mentally the final figure, which will be a 3, and the figure or figures then left will represent the number first thought of. For example:—
| The number thought of is | 11 |
| Multiplied by 3, it is | 33 |
| Add 1 | 34 |
| Multiply by 3 | 102 |
| Add the number (11) thought of | 113 |
The result of which, when told, will show 11 to be the number thought of.
| Second Method.— | Let any number be thought of, which we will again suppose to be | 11 |
| Instruct that it be doubled | 22 | |
| Instruct that some stated even number be added (say 54) | 76 | |
| Let the result be halved | 38 | |
| Deduct the number first thought of (11) | 27 |
The result will always be the half of the number that was instructed to be added.