INTELLECT SHARPENERS

Otago Daily Times, Issue 22213, 16 March 1934, Page 3

INTELLECT SHARPENERS

By C. J. Wherefore.

Written for the &tago Daily Times.

[Correspondence should be addressed to Box 1177, Wellington.] A BAIL WAY TICKET. Mr T. participated in a Sunday excursion to a certain country town, in which the return ticket cost only 60 per cent, of the usual single fare. During the day he met some old friends, who invited him to stay until Monday morning. One of these friends purchased from him the return half of his ticket for half the price he had paid for it, and travelled to town by the excursion train on its return journey. On Monday Mr T. returned to town, and took a return ticket at the usual rates, this being, of course, twice the cost of a single ticket. His friend, whom he afterwards met in town, purchased from him also the return half of this ticket, but Mr T. would accept only a round sum for it, which happened to be SO per cent, of the cost of a single ticket. The result of all this fraudulent buying and selling was that Mr T’s two railway tickets had cost him £t 17s 6d. What was the cost of the excursion ticket? A SUBSTITUTION PROBLEM. This problem is similar to the one given four weeks ago, but it is less difficult. Numerals have to be written in place of. the letters, so that the result is a sum in simple addition, and no two letters have the same numerical value. RAIN WIND STORM A REVISED VERSION. •?,. As I was going to St. Ives, . • I met a man and seven wives; - Every wife, you understand, Held a suitcase in her hand, And, every case a number bore From one to seven and no more. The sum of money each enclosed, Equalled-the number thus exposed, Expressed in pounds, it is implied, AM by a constant multiplied. The first and last together add To find how much the old man had. The average of all eight was then Just thirteen pounds and shillings ten. How much had each one of the eight, Is what you have to calculate.

A PROBLEM FOR METEOROLOGISTS. Mr S. has a rain gauge of five inches diameter standing on his.lawn. One day, during a long spell of dry weather, some of his friends, called on him, but found the house locked up and no one at home. They discovered a email mug hanging on a tap in the garden; it was cylindrical in shape, the depth being four inches and the diameter three inches. Each of these visitors filled the mug at the tap and emptied the contents into the rain gauge. Then they left a piece of paper under the front door, on which they had written: “We'left our cards in the rain gauge.” When Mr S. examined the instrument, he measured out the equivalent of 4.32 in of rain. The problem is to find how many persons there were in the party which called on him. .. .. ARMCHAIR PROBLEMS! A certain wool-grower says that the average weight of liis bales this year is expressed in pounds by three consecutive numerals. ' The highest price received for the wool makes the return for one-third of this weight equal a sum of money in which the numbers of pounds, shillings, and pence are the same, , What is the average weight of his bales, and what is the.(price per pound received? ■ % A neighbour of the gentleman mentioned above states that last year the average weight of his bales showed the same peculiarity, namely, that of being expressed by three consecutive numerals. But then the price' per pound was so much less, that if the weights of the bales had been only four pounds less, the money received for the whole bale would have been the same as that which his friend mentions as .having been received for one-third of a bale. What was the price this man received? Mr Black can drive his car. eight miles in the time required by Mr White to travel only.seven .miles. These gentlemen had several, matters of business to discuss, so they arranged a meeting by driving to a small town situated on the road between their two respective places of residence. Both of them left their homes at the same time, and arrived at the place appointed for the_ meeting at the same time. After discussing their business,.Mr Black drove straight back to his home, but Mr White drove to the house of a friend,nine miles away. From there he returned to the township, and then drove straight home. The result was that the two cars registered the same mileage as the amount of their days travelling. The problem is to find how far the township mentioned is from the homos of these two gentlemen. A PERPLEXING TIME TABLE. In order to travel from Arden to Dampley it is necessary to change trains at Bleakhouse, The railway stops at Clearwater, and the remainder of the journey has to be made by a service bus. Now trains leave Arden at 6,8, 10 a.m., and 12, 2, and 4 p.m., and they take two hours on the journey to Bleakhouse. They leave Bleakhouse at 7,9, 11 a.m., and 1,3, 5, and 7 p.m., and these also take two hours for the journey to Clearwater. The buses leave Clearwater at 8, 10 a.m., and at 12, 2,4, 6, and 8 p.m., and this journey also takes two hours. Readers are invited to discover in how many ways can a traveller arrange the whole journey during the interval between 6 a.m., when the first train leaves Arden, and 10 p.m. of the same day, when the last bus reaches Dampley. The number is much less than might be expected, because we have to consider only those trains and buses which the time table makes it possible for us to catch.

SOLUTIONS TO LAST WEEK’S

PROBLEMS.

Anagram.—Cleared, declare, rc-laccd. On Dairy Farm. —There were four children.

Clock.—On the morning of the fifteenth day . after his departure. Armchair Problems. — (1) He will be four •. times as old as bis daughter in 1035, and three times as old in 1039. (2) Two per cent. (3). Twenty-three persons, each of whom spent lid. (4) A block of writing paper containing 100 sheets for 6d and a package of 25 envelopes for 3d. A Bad Memory.—The first statement would mean that each side of the paddock was 77 miles in length. The second Would make the side less than four foot. It seems therefore that his memory is deceiving him in both cases.