If a milkmaid four feet ten inches in height, while sitting on a three-legged stool, took four pints of milk out of every fifteen cows, what was the size of the field in which the animals grazed, and what was the girl’s name, age, and the occupation of her grandfather? If thirty thousand millions of human beings have lived since the beginning of the world, how many may we safely say will die before the end of it? N.B.--This example to be worked out by simple subtraction, algebra, and the rule of three. Compare results. 72. Find two numbers in the proportion of 9 to 7 such as the square of their sum shall be equal to the cube of their difference. ARITHMETICAL THOUGHT READING. A great deal of fun can be derived from puzzles of this nature--they are endless in variety--and as they depend upon some principle in arithmetic should be easily remembered. Example 1. Think of a number, say 5 Double it 10 Add 5 15 Add 12 27 Take away 3 24 Halve it 12 Take away number first thought of--5 The answer will _always_ be 7 Example 2. Think of a number, say 8 Square it 64 Subtract the square of the number which is 1 less than the number thought of--that is 7--whose square is 49--leaves 15 Add 1 16 When this last number is told, halve it, and you will arrive at the original number--8. Example 3. Think of a number, say 9 Multiply by 3 27 Add 2 29 Multiply by 3 87 Add 2 more than the number thought of (11) 98 The number of _tens_ in the last answer gives the number thought of, viz., 9. Example 4. Think of a number, say 7 Multiply by 3 21 [If product be odd] add 1 22 Halve it 11 Multiply by 3 33 [If product be odd] add 1 34 Halve it 17 Ask how many 9’s are in the remainder, when, of course, the reply will be 1. The secret is to bear in mind whether the first sum be odd or even. If odd first time, retain 1 in the memory; if odd a second time, 2 more, making 3; to which add 4 for every 9 contained in the remainder.