A and B have an 8 gallon cask full of wine, which they wish to divide into two equal parts, and the only measures they have are a 5-gallon cask and a 3-gallon cask. How shall they make the division with these two vessels?
Method.—First fill the 3-gallon cask from the 8-gallon cask; then pour these 3 gallons into the 5-gallon cask; then fill the 3-gallon cask again, and fill the 5-gallon cask from the 3-gallon cask; this will leave 1 gallon in the 3-gallon cask; then empty the 5-gallon cask into the 8-gallon cask, pour the 1 gallon from the 3-gallon cask into the 5-gallon cask, and fill the 3-gallon cask from the 8-gallon cask. There will then be 4 gallons in the 8-gallon cask.
Two men in an oyster saloon laid a wager as to which could eat the most oysters. One ate ninety-nine and the other ate a hundred, and won. How many did both eat?
Remark.—The catch is on a hundred and won. When spoken it sounds as if it meant “one ate ninety-nine and the other ate a hundred and one;” hence, the result usually given is two hundred. The correct result is one hundred and ninety-nine.
If a room with 8 corners had a cat in each corner, seven cats before each cat, and a cat on each cat’s tail, what would be the whole number of cats?
Answer.—Eight cats.
Tell a person to think of a number, multiply by 3, multiply the product by 2, divide the result by 6, add 20, subtract the number thought of, divide by 4, and then tell him what his result is.
Method.—The result will be five. The reason is clear. By multiplying by 3 and 2 and dividing by 6 he has obtained the number thought of. Add 20, he has the number thought of, plus 20; then subtract the number thought of, and he has twenty. Now I know he has twenty; hence, I can tell him what he has if he divides by 4.
A farmer having an ox-chain consisting of 15 links, broke it into five equal parts, and took it to a blacksmith to be welded together. The blacksmith agreed to repair it for 50 cents for each welding; but when he presented his bill he charged for four weldings, making the bill $2.00. The farmer objected to the bill, saying that it should have been repaired with only three weldings. How was it to be done?
Method.—Each piece consisted of three links; cut open the three links of one piece and use these to connect the other four pieces of the chain.