INTELLECT SHARPENERS

Otago Daily Times, Issue 23447, 11 March 1938, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times By C. J. Wherefore

Correspondence should be addressed to Box 1177. Wellington,

MATHEMATICS OVER THE TELEPHONE

When Mrs C telephoned to me to come to tea at her new house m Makebelieve Terrace, she could hear me quite well, but I could not hear her. I had to ask her to repeat the number of her house, and even then it was not clear, so she added; “ Take the numbers of my two sisters houses, multiply them together, and subtract the number of the day of the month. Or divide one by the other, and add four times the number of the day. Either of these calculations will tell you my number.” I remarked that to-day is the twelfth, and she went on: “Quite right, and that is the difference between the numbers of my two sisters’ houses.” What is the number of Mrs C’s house? ARMCHAIR PROBLEM The answer to the following problem ought to be obvious, but I have to confess that I took out pencil and paper before I noticed this fact myself when a friend put the problem before me. Three men, A, B. and C, own some sheep. A’s number is equal to one-third of B’s plus two-thirds of C’s. ■ B’s number is equal to a quarter of A’s plus three-quarters of C’s, and C’s number is equal to one-eighth of B’s plus seven-eighths of A’s. How many sheep has each of the three men? NON-MATHEMATICAL PROBLEM In the lines given below the spaces are to be filled with three words, each of which differs from the others by one letter. The letter thus changed comes at the same place among the others, neither at the beginning nor at the end. Down came the rain, the public kept away, No hope was there our fete could now succeed. Let me . . . my tale, the folk, I say, Who kept the stalls, looked very sad indeed. But one did smile, she deigned with me to walk, We quite forgot the pretty things , . . Whilst we had tea together, and our talk Left all the money troubles quite . . . A SIMPLE PROBLEM IN AGES Uncle Bob took his three nieces to tea at the Primrose Tea Rooms. The girls’ ages are all different, and when added together they make 32. They sat at a square table, Marion opposite her uncle, Noel and Olive to left and right of him. The sum of the ages of the two girls sitting opposite one another is equal to that of the eldest, and the product of the same two ages is equal to the sum of the ages of Marion and her uncle. What do we know about Uncle Bob’s age? Is he an old man? ARGUMENTATIVE PROBLEM Five women, whose names are Alice, Beryl, Clare, Dora, and Ethel, are the wives of Andrew, Bill, Charles, David, and Edwin, but not respectively, that is, no married pair have the same initials. The problem is to arrange these ten individuals in pairs by examining the clues given herewith. Andrew lives in Invercargill, but Ethel, who is his sister, lives in Oamaru. His wife was formerly his typiste. I know Bill fairly well; he borrowed my lawn mower last Saturday. wife is a trained nurse. Charles has never met Bill or David or Edwin, and knows nothing about them. David is employed temporarily as manager of a back country station, and receives his mail only once a week, when he sends a man 15 miles to fetch it.

Alice lives in a flat, quite a pleasing home, but small. Beryl lives in Auckland. Occasionally she writes to me, and her letters are very interesting, but she has little time for corresponding with her friends, because she writes to her husband every day Clara is fortunate in having a comfortable income of her own. Dora is, a trained nurse., but all I know about her is that her handwriting is so illegible that some of her friends have advised her to learn typing. Ethel is much younger than her brother —only 18 years old, I believe. How are the five married pairs made up? SOLUTIONS OF LAST WEEK’S PROBLEMS Arrangement.—79s, plus 684, plus 321, make 1800. Tram Journey.—He issued 32 tickets, namely, 6,5, 6,7, 8, at the stations A, B, C, D, E, respectively. Armchair Problem. —A drove 28 miles to hotel, 36 to power station,. 12 to destination. B drove 21 miles to hotel, 27 to power station. 28 to destination. Cheque.—lt is probably obvious that the money was a number of pounds plus 19s lid. Therefore he worked 101 hours at 19d, for which he received £7 19s lid. Parting with Six Shillings.—Of course the cousin received the amount which was approximately 2s. It was Is lid and the other two girls were given Is 9d and 2s 4d. Counting Sheep.—Either he intended to buy 100 at 6s lid, and found three missing, or he expected 88 at 8s Id, and found five missing. These two solutions are to be expected, but there cannot be any more, because 8051 has only the two factors used.