INTELLECT SHARPENERS

Otago Daily Times, Issue 22355, 31 August 1934, Page 3

INTELLECT SHARPENERS

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

[Correspondence should be addressed to 'Box 1177, Wellington.] ANAGRAM. In the lines given below the four spaces are to be filled with words composed of the same six letters. ’ In the fourth line there is an “ s ” at the end of the word for reasons of grammar. I love my when its products stand All in brilliant rows of summer colour; I love it less when autumn takes command, No visions of a brain were duller. And when I dig it in its winter state. It stands in —— of my utmost hate. A NEW VERSION OF AN OLD PROBLEM. There is an old problem, which is found in many collections of puzzles, concerning an Arab who left 17 camels to three sons, who were to have one-half, onethird, and one-ninth of the number. The solution given is that the judge lent them one camel, so that they got 9,6, and 2 camels, then returned the one that was lent. Of course, this is quite inaccurate, and all good problemists find it very unsatisfactory, but no true answer could be given, because the three vulgar fractions added together are less than unity. The following problem is therefore submitted as an improvement: —The judge, having taken his degree at a university, had no hesitation in pronouncing the will to be inoperative, and ordered the camels to be sold. But he pointed out that the expenses, including succession and estate duties, would require oneeighteenth part of the sum received for the camels. He thought it the right thing to respect the wishes of the testator with regard to the heirs receiving one-half, one-third, and one-ninth of the money available, but these were to be fractions of the whole value of the estate before deducting taxation, Now the prices received for the camels were 17 consecutive numbers of pounds without. shillings, each son also received his share in whole numbers of pounds, and, of course, the sum paid in taxation was also a similar whole number. The problem is to find what prices were obtained for the camels, and how much money each of the sons received.

A PROBLEM FOR WIRELESS MEN. Four men, who are keen upon their wireless sets, live respectively in Auckland, Wellington, Christchurch ._ and Dunedin. For the purpose of this problem they are listening only to the four principal broadcasting stations in the four cities mentioned. During the evening no man has been listening to his own local station, nor has his own local station been received by a resident in the city of the station to which that man is listening at the hour to which this problem refers. Each of the four is now listening to a different station, and the puzzle is to find to which station each of them _ is listening. The Dunedin man is listening to the station to which the Christchurch man was listening half an hour ago, but not now. The Wellington man is listening to the station to which the Auckland man was listening half an hour ago, but not now. The Auckland man cannot “ get ” Dunedin. ALGEBRA IN THE KITCHEN. Miss Minerva went directly from school, where she had been receiving a lesson in algebra, to a cookery class, and she stems to have got her notes rather mixed. In the evening when she tried to write out fair copies her recipe for a two-pound cake was as follows: —The weight of Hour required is equal to the sum of the weights of butter and of sugar, and the number of cups of milk is equal to the difference between the numbers of pounds of butter and of sugar. The number of eggs is equal to the number of pounds of flour, butter, and sugar, added together, The number of teaspoonfuls of bicarbonate of soda is the same as the number of pounds of sugar, and the quantity of cream of tartar is twice this small amount. The problem is to reconstruct the recipe for a cake-'thus confused by imperfect r.otetakmg. A SPECULATION. ■Mr B. has just sold a section of land for £2OO. He bought it ten years ago for £IOO, and he feels that in doubling his money he has brought off a very profitable investment, although he has to admit that it. has cost him five pounds a year for rates and taxes. Do readers agree with Mr B. in thinking that he made a highly profitable speculation? SOLUTIONS OF LAST WEEK’S PROBLEMS. Flag Station. —At 65 and 35 miles from town. The Excursion Train. —One-tenth of a mile. ■ . ■ Cars and Sheep.—One and five-sixths miles per hour. Word Change.—Hard, ward, word, wore, sore, sort, soft. Armchair Problems. — (I) Half the sum of the two amounts mentioned, £127 15s, is the price received. (2) Increase 15 by one-tenth of itself, and result, 16J, is the percentage required. An Argumentative Problem. —As A shot one bird, which counted 3, his other five cartridges killed at least 5 rabbits. Therefore the- three equal scores were not less than 8. Then take B and C together, they scored 16 points, and cannot have killed fewer than 12 animals. This can happen in two ways: (1) Each man shot 2 hares, 4 rabbits, and (2) one man shot 3 hares, 2 rabbits, the other 1 hare, 6 rabbits. Both of these are clearly inadmissible. The only explanation is that one man got two rabbits with one shot, so we write 13 in place of 12, and start again. There is only one solution which is not contrary to specification, namely, that one man shot 2 hares, 4 rabbits, and the other 1 hare, 6 rabbits. As the two hares belong to B, the other lot belongs to C, and it shows the reason why heclaims to be the winner.

This is a love story from romantic Cairo. A student of that city loved beautiful 18-year-old Nabawia Hassanein, who lived in the house opposite. He demonstrated his affection by staging longingly at her window. Nabawia was not flattered. In fact, she showed her resentment of her would-be lover’s attentions by hurling a stone at him as he stood at his window. The stone hit him on the nose and broke it. Nabawia has been sent to prison for two years.