You can then tell him that if he will subtract from this the number he thought of, the remainder will be, in the case supposed, 2.
Note.—The remainder is always half the number you tell him to add.
To Discover Two or More Numbers that a Person has Thought of.
FIRST CASE.
Where each of the numbers is less than 10. Suppose the numbers thought of were 2, 3, 5.
| EXAMPLE. | |
| 1. Desire him to double the first number, making | 4 |
| 2. To add one to it | 5 |
| 3. To multiply by 5 | 25 |
| 4. To add the second number | 28 |
| There being a third number, repeat the process. | |
| 5. To double it | 56 |
| 6. To add 1 to it | 57 |
| 7. To multiply by 5 | 285 |
| 8. To add the third number | 290 |
And to proceed in the same manner for as many numbers as were thought of. Let him tell you the last sum produced (in this case, 290). Then, if there were two numbers thought of, you must subtract 5; if three, 55; if four, 555. You must here subtract 55; leaving a remainder of 235, which are the numbers thought of, 2, 3, and 5.
SECOND CASE.
Where one or more of the numbers are 10, or more than 10, and where there is an odd number of numbers thought of.
Suppose he fixes upon five numbers, viz., 4, 6, 9, 15, 16.