INTELLECT SHARPENERS

Otago Daily Times, Issue 23107, 5 February 1937, Page 3

INTELLECT SHARPENERS

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

Correspondence should be addressed to Box 1177. Wellington

NON-MATHEMATICAL PUZZLE In the lines given below the three spaces are to be filled with words, which differ from one another by only one letter. The letter which has to be changed comes at the same place in each word, neither at the beginning nor the end. In handing me your album, gracious friend, You made a most acceptable request, I must some verses that will tend To make you hear me at my very best. Your words my courage. Take these lines, And if you find them as you say you need them, Think of one, who his name now gladly signs, ■ him then where he may see you read them. WHICH PAGE IS IT? The man sitting opposite to me in the train closed his book, as we approached the station, but he studied the number of the page very carefully I, myself, was using a piece of paper as a book mark, and he judged it a suitable occasion to explain how he impressed the number on his memory. He stated that there are three figures, and the sum of them comes to 14, while the product of the first and ‘third, reading from left to right, is equal to the second one. “ Now,” he added, “ can you say what the number is? ” Can I, or can I not? A PROBLEM CONCERNING • BOOKS “ Here is an easy problem for you,” said my helpful friend. “A bookseller gave a number of books, which he had been unable to sell, to a canvasser to be disposed of, but he made it a condition that the price of any one book should not pe less than a certain sum, which he named. The canvasser asked all customers for a number of shillings without additional pence, but he was equally willing to sell, two books or seven, and for both these numbers the prices were also shillings without pence. All three of these amounts payable were such that, if stated in pence, the figures added together made 12. Now tell me at what prices he sold these lots of one, two and six, and what was the mir#ium he was permitted to accept as the value of one book? ” I objected to this that the purchaser of two books was getting better value for his money than the man who bought six; in -fact, he was getting the best bargain obtainable. “ That can’t be helped,” was the reply, “ and anyhow you can’t have your own way always.” What are the answers to the questions given above?

A BOARDING HOUSE PROBLEM My friend Mr F. tells me that when the boarders arrived for tea at Mrs Todger’s establishment last Sunday they found some freshlybaked cakes on the table. There were just 13 of them, and each one was marked with two grooves crossing it at right angles to one another, so that it could be broken into four equal pieces. The gentlemen. whose initials are A., 8., C.; etc., helped themselves in alphabetical order, and each one in his turn took a quarter of a cake more than the man who came before him. The average of the amounts taken by D and E was equal to the amount which each one would have received if all the boarders had taken equal shares. How much do you think my friend Mr F received?

ARGUMENTATIVE PROBLEM Mr Pickem was much interested in a race, in which five horses started —Benedick, Leonato, Claudio, Pedro and Dogberry. Unfortunately he arrived at his club too late to hear the news over the wireless, and when he asked his friends about the result, they seem to have made fur of him, instead of giving him the information required. Mr Smith said Leonato was secpnd, and Benedick third. Mr Jones said Pedro was first and Claudio fourth. Mr Williams backed up his friend in saying Claudio was fourth, but was sure that Pedro was third, not first. Mr Brown said Leonato was second and Dogberry fourth, while Mr Robin son agreed with him that Dogberry was fourth, but was quite sure that Benedick was first. 'Mr Pickem says that his friends are infallible liars, but in this he is wrong, because each one has made one statement true and one untrue. Can he discover the real order of the five horses from what he has been told?

SOLUTIONS OF LAST WEEK’S PROBLEMS Word Change.—Soon, moon. morn, more, fore, fare, fate, late. Childish Problem. —A gave three threepenny pieces, and B six shillings, M gave nine pennies and N 12 sixpences. Aerial Photos.—The clue is that the paddock C, which is seen in both photos, must have a multiple of 11 animals in it. When 33 is tried, the rest is easy. There are 21, 15, 33 27, 17, in A. B. C. D. E. respectively. Home Work.—The boys obtained 26 and 30 marks out of a possible 50. But this is the result of common sense rather than of calculation, because the equation which the girl mentions has more than one solution

Second-hand Cars.—N. drove 26 miles further than M., namely, 113 miles, compared with 87. After this it is easy to see that the prices were £ll3 2s and £lO7 7s. And of course the problem could be solved equally well by tackling prices first and mileages afterwards.

Bazaar.—Miss A must have sold at least one half lot, that is, three baskets for 7d, but of course she did not transgress the conditions mentioned in the bet by doing so. As we do not know which was the more successful saleswoman, we have to admit two solutions. (1) 'V sells 3J Jots at 14d, B three lots at 16d (2) A sells 4J lots at 14d, B 4 lots at Hid.