INTELLECT SHARPENERS

New Zealand Herald, Volume LXXIII, Issue 22344, 15 February 1936, Page 5 (Supplement)

INTELLECT SHARPENERS

By C. J. WHEREFORE

• ARMCHAIR PROBLEM Mrs. A entered a train at a flag station, and handed to the guard a ten shilling note to pay for her ticket to town. He had no change, bo she took back the note, and gave him a number of shillings, which was all the silver she had, and some pence, which she borrowed from her friend Mrs. B. When the guard had gone, Mrs. 33 explained that she had joined the train at a flag station a little farther from town, and that the money she had lent to Mrs. A, was the change which the guard had given to her for her own ten shilling note. What is the smallest amount by which the cost of Mrs. B's ticket can have exceeded that of the other ticket? PHOTOGRAPHER'S PROBLEM An amateur photographer took a negative to a dealer to be enlarged. It was a picture of a group of persons, all of whom were so much interested, that they wanted copies. The result was that a number of enlargements had to be made, and when the time came for settling the account, the photographer found that it showed the same number of pence as the quotation for one copy, but the number of shillings had crossed the frontier and now stood in the pounds column. What was the price charged for each copy, and how many copies were made ? THE NUMBER OP THIS YEAR A correspondent, writing from Auckland, comments upon a problem published on January 4, in which it was remarked that 1936, the number of this year, is the square of 44. The last time this happened, in 1849, gave De Morgan the opportunity to say that his ago was X years in the year X squared. No such opportunity can occur again until 2025, but two simple questions of the same nature may be askod. What is the next 3'ear, of which the number is a power, but not a square of a number? And what is the next year, of which the number is the sum of two squares, if the square of 1 be considered inadmissible, so that 1937 may not be used in this manner? PROBLEM IN AGES "I Jiave just been to tea with my three girl cousins," said Professor Aftermath. "That must have been a pleasant experience," I replied, "how old are they?" He did not appear to notice my question, and continued his own story. "A few weeks ago somebody gave each of them money-boxes, I assure you I had nothing to do with it. Each of the?e boxes hold 80 sixpences, and cannot be opened until it is full, at least not by honest means. Now these girls have accumulated only a 100 sixpences altogether. Alice has been saving at the rate of one and a quarter shillings for every year of her age, Brenda has one and one-third shillings for overy year of her age, and Cicely has as much as one shilling and sixpence for every year of her age. No two of them have the same amount, but two of them have come rather near to doing so. Now, my friend, you asked a frivolous question a minute ago. I answer you seriously that the three >iges together add up to 35, and if you want to know the answer to your question, you can find it yourself with a little concentrated thought." • BORROWER AND CREDITOR There are two borrowers, Claude and Ernest, schoolboys, who want a new valve for the wireless set they have made themselves. The creditor is Ernest's sister, Muriel, who is very tar from being keen to lend the money, and will do so only if they pay her nearly the whole of their pocket mont>y

every week, until the debt is extinguished. The valve costs Bs. 4d. f and Ernest has six times as much capital as Claude, which showß that the hoys are equally good at, saving, because Ernest's weekly allb «vance is exactly six times as much as that of his friend. Like other persons who borrow money, they have no alternative but to accept the creditor's terms, which are that Ernest shall pay her all his weekly income except one penny, and Claude must do the same, retaining only one half-penny. This is the only fractionof a penny in the business, and the amount of the loan will be repaid by an exact number of these weekly instalments. How much has each of the boys contributed to the price of the valve, and how much have they borrowed from Ernest's sister P SPORTING INFORMATION Grandfather was very keen to hear the result of one particular race, in which he had put some money on a horse called, The Friar. Unfortunately the wireless was working bo' badly, that he himself could distinguish nothing, and his grandchildren were either equally unsuccessful, or were unwilling to help him. This is what he told me. "John x says, Locksley was first and Cgdrio third. Keith says, Cedric was second and Athelstane fourth. Leslie says, not Athelstane, but Howena was fouth, and that Cedric came in fifth. Muriel says, Athelstane was third and Locksley second, and Noel is sure that Locksley was first with Cedric fourth, not fifth as his sister says. Not one of them can tell me anything about The Friar.'? I assured the disappointed man that each of his grandchildren had told him one thing that was true and one thing that was untrue, and that with t.hia information he had all he required to show in what order the horses, including The Friar, had been placed. What was this order? SOLUTIONS TO PROBLEMS PUBLISHED FEBRUARY 8. Problem in Ages.—She cannot be more than 29 years old. Breakfast Time.—lt is impossible to ascertain the errors of any of the watches, but they were all certainly slow. Therefore, the real time was after 8 a.m., and that is the only question asked. At a Restaurant. —It is not difficult to see that there were either 23 persons for 19 days or 19 persons for 23 days. That the second solution is the correct one can only be derived from the last remark given as a pretended afterthought. A Pet Sheop.—lf A has more sheep ihat C, he has either twice as many, or he has 80 sheep to C's one. He denies the first statement, therefore, the second is correct, andsC must be the owner of the pet. ? Armchair Problem.—As the payment is 50 sixpences, the problem is to divide this into three parts, which are nearly, but not exactly, equal. The only solution admissible is 15, 17, 18, and it follows that the three weekly salaries must be £2 ss, £2 lis, and £2 14s. Argumentative Problem. —Duncan cannot be one of the brothers, because he is an old man recently arrived in New Zealand. The owner of the Podge cannot be one of them, be cause he is married, nor can the owner of the Chevrolet, because ho has a sister, who is not the sister of anyone else. Therefore, Aliek and Fred are the brothers, and are owners of the Ford and Austin respectively. Duncan is an aged man, and he cannot be either, the married man or the brother-in-law, therefore, he is the owner of the Buick. Charles cannot own the Chevrolet, therefore, he owns the Dodge, and Ben owns the Chevrolet.