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.
The Three Travelers.
Three men met at a caravansary or inn, in Persia; and two of them brought their provisions along with them, according to the custom of the country; but the third, not having provided any, proposed to the others that they should eat together, and he would pay the value of his proportion. This being agreed to, A produced 5 loaves, and B 3 loaves, all of which the travelers ate together, and C paid 8 pieces of money as the value of his share, with which the others were satisfied, but quarreled about the division of it. Upon this the matter was referred to the judge, who decided impartially. What was his decision?
At first sight it would seem that the money should be divided according to the bread furnished; but we must consider that as the 3 ate 8 loaves, each one ate 2 2/3 loaves of the bread he furnished. This from 5 would leave 2 1/3 loaves furnished the stranger by A; and 3 - 2 2/3 = 1/3 furnished by B, hence 2 1/3 to 1/3 = 7 to 1, is the ratio in which the money is to be divided. If you imagine A and B to furnish, and C to consume all, then the division will be according to amounts furnished.