How Many Counters Have I in My Hands?
A person having an equal number of counters in each hand, it is required to find how many he has altogether.
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 three 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 four be transferred, the hands will contain 6 and 14.
He will divide 14 by 6 and inform you that the quotient is 2 1/3.
You multiply 4 by 2 1/3, which is 9 1/3.
Add four to this, making 13 1/3 equal to 40/3.
Subtract 1 from 2 1/3, leaving 1 1/3 or 4/3.
Divide 40/3 by 4/3, giving 10, the number in each hand.