To conceal the artifice better, it will be sufficient to ask whether the sum of the two products can be halved without a remainder--for in that case the total will be even, and in the contrary case odd. 222. Which is the heavier, and by how much--a pound of gold or a pound of feathers; an ounce of gold or an ounce of feathers? 223. Plant an orchard of 21 trees, so that there shall be 9 straight rows with 5 trees in each row, the outline to be a regular geometrical figure. SETTLING UP. 224. A person paid a debt of £5 with sovereigns and half-crowns. Now, there were half the number of sovereigns that there were half-crowns. How many were there of each? A “CATCH.” | | | | | | | | | | | | | | | | | | | | 225. How can you rub out 20 marks on a slate, have only five rubs, and rub out every time an odd one? 226. From six take nine, from nine take ten, From forty take fifty, and six will remain. 227. A man and his wife lived in wedlock, one-third of his age and one-fourth of hers. Now, the man was eight years older than his wife at marriage, and she survived him 20 years. How old were they when married? TO PROVE THAT YOU HAVE ELEVEN FINGERS. Count all the fingers of the two hands, then commence to count backwards on one hand, saying, “10, 9, 8, 7, 6” (with emphasis on the _6_), and hold up the other hand saying, “and 5 makes 11.” This simple deception has often puzzled many. 228. A man travelled a certain journey at the rate of four miles an hour, and returned at the rate of three miles an hour. He took 21 hours in going and returning. What was the total distance gone over? 229. From what height above the earth will a person see one-third of its surface? 230. The difference between 17/21 and 11/14 of a certain sum is £10. What is the sum? 231. What decimal fraction is a second of a day? 232. Two trains are running on parallel lines in the same direction at rates respectively 45 miles and 35 miles an hour; the length of the first is 17 yds. 2 ft., and of the second 70 yds. 1 ft. How long will the one be in passing the other? 233. Suppose a bushel to be exactly round, And the depth, when measured, eight inches be found; If the breadth 18·789 inches you discover, This bushel is legal all England over: But a workman would make one of another frame, Seven inches and a half the depth of the same; Now say of what length must the diameter be, That it may with the former in measure agree. WORTH TRYING. A well known writer on mathematics, and a member of the Academy of Science, Paris, says that the most skilful calculator could not in less than a month find within a unit the cube root of 696536483318640035073641037. A PROBLEM THAT WORRIED THE ANCIENTS. Many profound works have been written on the following famous problem:-- “When a man says ‘I lie,’ does he lie, or does he not? If he lies he speaks the truth; if he speaks the truth he lies.”