INTELLECT SHARPENERS

Otago Daily Times, Issue 22823, 6 March 1936, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Times. By C. J. Whekefore. [Correspondence should be addressed to Box 1177. Wellington.] CORRESPOXDEN'CE. Alice and Brenda are the wives of Dick and Edward, and they are absent from their homed, visiting their sister, Constance. Her husband, Frank, is absent from his home, so that there arc three wives writing letters to their husband, who write in reply, but no husband writes quite as many letters as his own wife. In fact the total of letters written by the husbands is seven less than that of the wives' letters. Brenda has written two more than Alice, and Constance has written four more than Brenda, but at present her total is four less than that of her two sisters together. Edward has written two more than Dick, and Frank three more than Edward. How many letters has each of these six persons written? MANY INITIALS. A correspondent, writin.pt from an address, which cannot be found upon a map, asks a question concerning an advertisement. The (roods offered are tapes, having groups of letters woven in them, and arc intended to be stitched to clothing for showing the owner's initials. Supposing that such a firm proposed to keep in stock a sufficient number to supply any three initials, how many different tapes would they require? For the pur pose of the problem two alternatives maybe considered. First, let all three letters be different, and, second, let one lettei of the three be repeated, so that only two of them are really different. How many tapes would be required for each of these cases? COLLECTING STAMPS. I had to send four packages to England, and each of them required sixpence for postage. As the recipient is a stamp collector, I obtained eight stamps of different values, and put the correct amount on cacli of the four packages. How was this done? ARMCHAIR PROBLEM. Mr M. drove from Stratford to Endleigh, and the journey took just 36 minutes. When he returned, he was accompanied by hi s cousin, and apparently the time spent in talking to her prevented him from driving quite so efficiently as before. At any rate, his speed was now one mile per hour less than on the previous journey, and the time required w-as ij minutes longer. How far apart are the two towns? A ROMANTIC PROBLEM. Edwin gave Angelina a present on the day their engagement was announced. It was not at all a valuable article, but on the day of their wedding he gave her another, which cost him the price of the former one multiplied by the number of months which had elapsed between the two dates. The two presents together cost him £l4, and in each of the prices paid there was an odd sixpence. For how many months were they engaged? Be careful. A NON-MATHEMATICAL PROBLEM. There are four children at that farm — Stanley, Tom, May, and Ruth. They ride to school on ponies named Sandy, Maggie, Towser, and Roy, and they seem to like changing, for they seldom ride the same ponies on two consecutive days. To-day not one of them arrived at the school riding a pony whose initial is the same as that of his or her own name. With May it is not merely a case of initials: the two names had not one letter in common. The girls can do what they like with Roy, but he does not like either of the boys. Tom never rides him; in fact, the pony will not let him mount. Stanley can ride him, but dislikes doing so, and always takes another pony if he can. The question is, did Stanley ride Roy to-day? SOLUTIONS OF LAST WEEK'S . PROBLEMS. Pronunciation.—Threat, thereat, great, treat. Gardening.—The sides were 51, 45. 24 feet and 26, 24, 10 feet. Substitution. —The smallest numbers of yards of A, B, C, D, E are 2,3, 4,5, 6 respectively, and the L.C.M., 60, is the number of pence the man wished to spend. It is obvious that E cost lOd per yard, therefore F and G cost 9d and 8d respectively, and he got his seven yards by taking 4 of F and 3 of G'. Case. —The rule is to take the product of any two areas and divide by the third area. The quotient is the square of one of the dimensions required. By arranging the cancellation conveniently, this may be no more than armchair arithmetic. Thus, if 144 and 80 be placed above the line and 45 below it, the 45 may be made to disappear, leaving 16 x 16 in the numerator. Armchair Problem. — (1) This is absurdly easy, because it is evident that the numbers of men and children must have been equal. As the wives have to be accounted for, there were 20 each of men, wives, and children. (2) This is more 6erious, perhaps, but the difference must be either 25 or 0, and, as the guesses were nearly right, the meaning mtust be that there was no difference.