INTELLECT SHARPENERS

Otago Daily Times, Issue 23830, 9 June 1939, Page 3

INTELLECT SHARPENERS

Written for the Otago Daily Time? By C. J. Wherefore ANAGRAM In the lines given below the three spaces are to be filled with words composed of the same letters. With manners so . with face so stern, When in his office every day, His typiste feels she would not like to earn Such words of harsh rebuke as he might say. But some, who see him in quite different places, Have him for his very lenient mood, And told him that the true and actual case is, He could not scold a woman, if he would. A SUNDAY AFTERNOON PROBLEM The porter employed at the Fern Porch Private Hotel has a habit of thinking about the permanent guests by the numbers of their rooms, rather than by their names. Last Sunday three of the men asked him to ring up a garage that could supply three cars, and each of these men took out a lady for a drive What he noticed was that the men’s rooms were three consecutive numbers, and the ladies’ rooms were also consecutive numbers. And it was also true that when they had formed themselves into pairs, the sums of the two numbers in these three pairs made three consecutive numbers. The house is not a large one, there are not 100 rooms in it; in fact, these six numbers taken togethei came to only 114. How were the three pairs formed? SUBSTITUTION PROBLEM “I think these substitution problems are too easy,” said Professor Aftermath to his friend, Dr Doolittle. “Now here is a better one. I take a word of six letters, and number these letters from left to right 1,2, 3,4, 5, 6. Then the number represented by ONEO is a square. Can you tell me what it is? ” The doctor replied that he could not miss it, and added: “You will notice that NEO is also a square.” “Why, so it is,” said the professor, “ and EON is another square.” What are the three squares of which these learned men are speaking? TWO ARMCHAIR PROBLEMS Mr Neil and Mr Angus had bought some sheep at the saleyards, and they boxed their mobs to drive them home together. Mr Neil’s number was a little larger than the other, in' fact it was. a quarter more than those of his friend. When passing a neighbour on the road, they told him that there were “just over a hundred sheep there.” This was of course a round number, but what was the correct total? Four persons went to the pictures together. Bessie is two years older than Alfred, Charles is two years older than Bessie, and Dora is two years older than Charles. The eldest and youngest had seats, together in one row, and the other two sat together in another row. The result was that the product of the ages of one pair sitting together differed from that of the other two ages by a certain amount. What was that amount? DEALING WITH A DEFICIT Miss P, the' secretary and treasurer of our Literary Society, told me that her annual report: showed a small loss, which came to a few shillings without additional pence, but it was such a trifling sum that she knew several members would quite willingly make it up. Three persons had already made offers, without asking how much the deficit was. She said that if she took two-thirds of A’s offer, with half of B’s and a quarter of C’s, she would have exactly what was required. She added that she was unwilling to take anything from C. who had been rather rude about it, and she could decline his help, if she took all that the other two had offered. But she told me that she could afford to smile at C’s bad manners. What was the amount of the deficiency, and how much had each of the three members offered? AJso what was it that made her smile? SOLUTIONS TO LAST WEEK’S PROBLEMS Armchair Problem.—James Is aged 30 years, Josephine 25. Non-mathematical.—“ Why don't you speak for yourself, John?" Week-end,—The cheese costs Is Id per lb in any case, but for bread and butter there are two solutions. (1) Loaves at 3d, butter at Is 4d, (2) Loaves at 7d, butter at lid. Which prices are the more probable is not a question of mathematical work. Short Problem.—lt would not make any difference to the amount left in Tom’s possession, but it would make a great deal of difference to the amounts paid for tobacco and bicycle. It does not matter what his salary may be, but if ft be taken as £1 ?s 2d, for convenience, the payments are Is 2d and 3s, in the one case, and 3s 2d and Is in the other. Group Problem.—Four different men can be selected out of six in 15 different ways, but it is also unexpectedly true that the number of four-letter words obtainable is also 15. A is included in all these, so that the man with this initial would prefer the wordless method. E included in 10 words, and this is also the number of times any man would be employed, if chosen by the wordless method, so that E may be indifferent as to which method is chosen.