Note.—The remainder is always half of the number you tell him to add.

TO DISCOVER TWO OR MORE NUMBERS THAT A PERSON HAS THOUGHT OF.

1st 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 making4
2. To add 1 to it5
3. To multiply by 525
4. To add the second number28

There being a third number, repeat this process—

5. To double it56
6. To add 1 to it57
7. To multiply by 5285
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.

2d 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.