After the person has fixed on a number, bid him double it, and add 4 to that sum; then let him multiply the whole by 5, and to that product add 12; desire him also to multiply this sum by 10, and after having deducted 302 from the product, to tell you the remainder, from which, if you cut off the last two figures, the number that remains will be the one thought on.
Example.
| Let the number thought on be | 7 | ||
| Then the double of this is | 14 | ||
| And 4 added to it makes | 18 | ||
| This multiplied by 5 is | 90 | ||
| And 12 added to it is | 102 | ||
| And this multiplied by 10 is | 1020 | ||
| From which deducting | 302 | ||
| There remains | 718, | — |
which, by striking off the last two figures, gives 7,—the number thought on.
To tell the Number a Person has fixed upon, without asking him any Questions.
The person having chosen any number in his mind, from 1 to 15, bid him add one to it, and triple the amount. Then,
If it be an even number, let him take the half of it, and triple that half; but if it be an odd number, he must add 1 to it, and then halve it, and triple that half.
In like manner let him take the half of this number, if it be even, or the half of the next greater, if it be odd; and triple that half.
Again, bid him take the half of this last number, if even, or of the next greater, if odd; and the half of that half in the same way; and by observing at what steps he is obliged to add 1 in the halving, the following table will shew the number thought on:
| 1—0—0 | — 4— 8 | |
| 2—0—0 | —13— 5 | |
| 3—0—0 | — 3—11 | |
| 1—2—0 | — 2—10 | |
| 1—3—0 | — 8— 0 | |
| 1—2—3 | — 6—14 | |
| 2—3—0 | — 1— 9 | |
| 0—0—0 | —15— 7 |