| Suppose he fixes on | 8 |
| He must add 1 to it, making | 9 |
| Triple it | 27 |
| Halve it[11]—1st halving—(larger half) | 14 |
| Triple it | 42 |
| Halve it—2d halving | 21 |
| Triple it | 63 |
| Halve it—3d halving—(larger half) | 32 |
| Triple it | 96 |
| Halve it—4th halving. | 48 |
He need not inform you that 48 is the figure produced, but he must let you know in which of the four halvings he was obliged to take a "larger half;" having ascertained this point, you discover the number fixed upon in the following manner. Carry in your mind, or on a slip of paper, the following list of names in which the letter a occurs in one or more of the three syllables of all except the last.
The three syllables are intended to represent the 1st, 2d, and 3d halvings, and the occurrence of the letter A corresponds to the occurrence of a "larger half" in one or more of these three halvings. Having been informed where the larger half was taken, refer to the word which has A in the corresponding syllable, and against it stand two numbers, one of which was the number thought of; and of these two, the right hand number is the correct one if a larger half was taken in the 4th stage, and the left hand one if the, 4th halving was exact.
In the example given, a larger half occurred in the 1st and 3d stage; this points us to Car-ro-way, and the halving in the 4th stage being exact, shows us that 8 was the number fixed upon.
| If the 4th halving is exact. | If a larger half occurs in the 4th halving. | |
| WAsh-ing-ton | 4 | 12 |
| LA-fAy-ette | 2 | 10 |
| CAr-row-wAy | 8 | 0 |
| MAn-hAt-tAn | 6 | 14 |
| Ger-mA-ny | 13 | 5 |
| Tel-e-grAph | 3 | 11 |
| Bo-nA-pArte | 1 | 9 |
| Long-fel-low | 15 | 7 |
It will be observed that there is always a difference of 8 between the numbers of the columns, so that it is necessary to recollect only one of them. Perhaps some of our readers who wish to be adepts in this game, would prefer recollecting the above table if put in this form:
2-3 1-2 3 1-2-3 1-3 2 none
——————————————
1 2 3 4 8 13 15
where the upper line denotes the cases in which the "larger half" was taken, and the lower line the numbers of the left hand column above given.
Another Method.