Suppose he has 16 counters, or 8 in each hand. Desire him to transfer from one hand to the other a certain number of them, and to tell you the number so transferred. Suppose it be 4, the hands now contain 4 and 12. Ask him how many times the smaller number is contained in the larger; in this case it is 3 times. You must then multiply the number transferred, 4, by the 3, making 12, and add the 4, making 16; then divide 16 by the 3 minus 1; this will bring 8, the number in each hand.
In most cases fractions will occur in the process: when 10 counters are in each hand, and if 4 be transferred, the hands will contain 6 and 14.
He will divide 14 by 6 and inform you that the quotient is 22/6 or 21/3.
You multiply 4 by 21/3, which is 91/3.
Add 4 to this, making 131/3, equal to 40/3.
Subtract 1 from 21/3, leaving 11/3 or 4/3.
Divide 40/3 by 4/3 giving 10, the number in each hand.
THE MYSTERIOUS HALVINGS.
To tell the number a person has thought of.
One of the company must fix upon any one of the numbers from 1 to 15; this he keeps secret, as well as the numbers produced by the succeeding operations: