Two-thirds of six is nine, one-half of twelve is seven, the half of five is four, and six is half of eleven.
Method.—Two-thirds of SIX is IX, the upper half of XII is VII, the half of FIVE is IV, and the upper half of XI is VI.
Two men have 24 ounces of fluid which they wish to divide between them equally. How shall they effect the division, provided they have only three vessels; one containing 5 oz., the other 11 oz., and the third 13 oz.?
Method.—The method is similar to the division of 8 gallons in the question on page 78.
Three persons own 51 quarts of rice, and have only two measures; one a 4-quart, the other a 7-quart measure. How shall they divide it into three equal parts?
Method.—One-third of 51 is 17; so each must have 17 quarts. To measure 17 quarts fill the 7-quart measure twice and pour into some large vessel, making 14 quarts; then fill the 7-quart measure, draw off 4 quarts in the 4-quart measure, and then pour the remaining 3 quarts in the vessel containing the 14 quarts.
Think of a number composed of two unequal digits, invert the digits, take the difference between this and the original number, name one of the digits and I will name the other.
Method.—The sum of the digits in the difference is always nine; hence, when one is named the other equals 9, minus the one named.
Take any number, consisting of three consecutive digits and permutate them, making 6 numbers, and take the sum of these numbers, divide by 6, and tell me the result and I will tell you the digits of the number taken.
Method.—The quotient consists of three equal digits; the digits of the number taken are: 1st. one of these equal digits; 2d. this digit increased by a unit; 3d. this digit diminished by a unit. The same principle holds when the digits of the number taken differ by 2, 3, or 4. It is a very pretty problem to prove that the sum is always divisible by 9 and 18.