INTELLECT SHARPENERS

Otago Daily Times, Issue 22905, 12 June 1936, Page 2

INTELLECT SHARPENERS

Written for the Otago Daily Times.

By C. J. Whebefobe.

[Correspondence should be addressed to Box 1177. Wellington.]

WORD CHANGE. In the lines given below the spaces are to be filled with a series of words, each of which differs from the one before it by one letter, making the last word quite unlike the first, and with exactly the opposite meaning:— The air is , and traces of a frost Are upon the garden, where it seems The I put there recently, is lost, Never to • my mind with pleasant dreams. For winter comes, and gardeners understand That tlfcn they no impulse or desire To seize their spades, but rather take in hand A shovel to put on the fire. These verses should be of clues for you, And if they're , I'm really sorry too.

KEEPING A PROMISE. _ Tom was riding a very old and shabby bicycle. Now I had seen his two sisters pass my house on the way to the offices where they work n few minutes previously, and they were riding rather good machines. I asked the boy. therefore, if he was willing to tell me how much he had paid for his own unsightly article. He replied that what I probably wanted to know was what each of the three bicycles had cost, and he promised to tell me, but this is what he said: "The three together cost £lB, and none of us had to hand over any shillings or pence. The price of mine, increased by one-sixth of the price of Lucy's and one-ninth of that of Joan's would make twice the price of m:ne." Did he really keep his promise to give me the information of which he spoke?

A COMPLETE CURE. Professor Marvel has been sent to a seaside resort for his period of convalescence after an illness, the result of excessive mental arithmetic. The other day he pointed to three of his friends on the beach, and remarked: "The ages of these three boys are 12, 14, and 16. You can multiply the three ages together and also add them, then when you divide the greater by the less the quotient is four times the age of the eldest." The man who was pulling the bath chair was so much impressed that he made no answer, and the invalid repeated all he had said. This time he received a reply. " Oh, now I understand you. I thought you said it was 14 times the boys' nge, and, of course, that must be impossible." But the professor insisted that it is not at all impossible, and that it really would happen in so many years' time. The number of years which he mentioned has been omitted here, 60 that readers may have the satisfaction of finding it for themselves.

ANOTHER PROBLEM IN AGES. Miss Counter tells me that she and her sister, who is a few years younger than she is, went to a shop to buy some handkerchiefs. Her sister soon found what she wanted at a certain price, but she herself preferred some that were a penny cheaper. She purchased one more than her sister, and spent sixpence less money. Then she became more communicative, and added that the difference between the number of pence paid for each handkerchief and the number of them she took is equal to the difference between her own and her sister's ages. The difference deduced in the same manner with regard to her own bargain is more, but the product of the two differences is just equal to her own age. What are the ages of these two sisters?

SUBSTITUTION PROBLEM. A wealthy man had left a will which bequeathed his property to certain relatives, but only on condition that they should succeed in opening hie safe. This was secured by a combination lock, which showed seven letters in a row, all of them capable of being changed, and the problem was to form a simple word of seven letters. In this the heirs failed, and had to accept an alternative, in which they were permitted to open an envelope containing a clue, but for this they had to forfeit 5 per cent, of their fortune to an undeserving charity. The envelope contained the substitution puzzle shown below, in whicn numbers had to be written in place of the letters, so ns to make a sum in simple addition. They were informed that the word which would open the safe consisted of the letters corresponding to the numerals 7532804. They were able to find the word by solving this puzzle, and readers are now invited to do this also. FOUR FIVE NINE ARMCHAIR PROBLEM. Two men, A and B, went into camp for a week's fishing. Neither of them is at all truthful, but they recognise the necessity of telling the same story, and for this reason they had their statements prepared and rehearsed before they returned. One man, they said, had been continuously more lucky than the other,, and had always caught seven fish for every five obtained by his friend. They had fished every day of the seven, and had caught the same number every day. These statements are quite true, but they agreed to exaggerate their numbers, and in this they took care to be consistent by increasing their totals by the same percentage. How many fish did they really catch, and how many did they tell their friends they had caught?

SOLUTIONS OF LAST WEEK'S PROBLEMS. Postcard.—The person who wrote the card won with 16 points against 15 and 10. v . Modern Version.—lf A was as hard up as he said he was, he may have had only £l, then B must have had £SO. Musterers. —When the two statements are straightened out the result is a simple exercise in vulgar frnctions, showing that nine sheep were missing. Rhyme.—The endings of the lines should be: —Came, us all, the same, hall, forget, set. The words in the spaces are:— Ether, there,' three.

Armchair Problems. — (1) This is much easier than it looks, because the number of miles is certainly a multiple of 7, and is at once suspected of being a multiple of 5. Therefore 35 is tried, and is found to fit perfectly. (2) There were 96 books. (3) The excess over 100 is either 5 or a multiple thereof, and it is found that 105 sheep can be taken across under the conditions described.