INTELLECT SHARPENERS

Otago Daily Times, Issue 23505, 20 May 1938, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C. J. Wherefore Correspondence should be addressed to Box 1177, Wellington. PROBLEM IN AGES Our new neighbours, in the house to the right of our own, have four children. There are two girls, Alice and Barbara, and two boys, Charles and Douglas. No two of the ages are the same. If you subtract four times the elder girl’s age from eight times that of her sister, you get the same remainder as you have when you subtract five times the younger boy’s age from seven times that of his brother. Now what are the four ages? This problem was actually proposed to me by a friend, and I have to confess that it took me more time than I expected to find the answer. ANOTHER PROFESSORIAL PROBLEM At the Hotel Magnifique there is a telephone in every room, but owing to some error in the wiring, the numbers of these telephones on the hotel switchboard are always 10 more than those of the rooms themselves. Professor Aftermath told me that he stayed at this hotel with his secretary-daughter, and he offered me the following problem: “ The number of my daughter’s telephone, when divided by that of my own, gave a quotient only one more than the number of my own room. But when we divided the number of her room by mine, the quotient was no less than twice the number of my room. Now what were the numbers of the rooms we occupied? ” ARMCHAIR PROBLEM Mrs M and Mrs P bought two dozen eggs at the store, but they did not take equal shares of this number. On the contrary, Mrs P took a great deal more than Mrs M. The storekeeper had only a few left, less than a dozen, and he made a present of these to his two frequent customers. Mrs P said to her friend: “ If I should take all these additional eggs my number would be twice what yours would be if you took them.” Mrs M replied: “That is not a good way of putting it, because obviously we cannot both have the extra number. But if you take some of them and I take the rest, we shall have the same result, namely, that you will have twice as many eggs as I shall have.” How many eggs did they buy, and how many of the additional number did they take? WEEK-END CLUBS The members of two week-end clubs, one composed entirely of men and the other of women, had arrived at the same town, and the proprietor of a restaurant near the station had undertaken to provide breakfast for both parties at the same price per head. The treasurer of the ladies’ club met the other treasurer and showed him sevenpence, which was the amount of change she had received after handing the cashier a number of £1 notes. The men’s secretary told his friend that he had also paid over a number of notes in the same way, and what he said was; “ Our party consists of twice as many persons as yours and 11 more, and I received only one penny as change. How many persons were there in each party, and How much were they charged for fheir breakfast? SIXPENCE WORTH There were three boys and three girls, who found on a main road a purse containing three. shillings worth of silver and copper. As the motorist, who had lost it, was probably 100 miles away by this time, they divided the small amount among themselves in equal shares, but no two of them had exactly the same number of coins. There were halfpence among these, but no farthings. One boy had as many as the other two put together. One girl had as much as three times the number held by one of the other girls. What were the coins allotted to each of the six? SOLUTIONS OF LAST WEEK’S PROBLEMS Refreshments—There were only two persons in the car. Silver.—A, B, C had articles of value £72, £96, £54 respectively. Excess Fares. —A paid 4s 6d, plus 9d excess, B paid 4s Bd, plus 7d excess. C paid 4s 9d, plus 6d excess. Armchair Problem. —He held the larger amount in the right hand, but it is not necessary for him to have more than 4d in one hand and 3d in the other. Substitution. —The sum was £9 16s, and 196 is the square of 14 The time 20 minutes later was 9.36 a.m., and 576 minutes is the square of 38. Motoring.—The whole distance was 64 miles, of which one man drove 32 miles and the other 28, But I do not know which of them had the longer journey, because I did not wait for the last clue.