NUTS TO CRACK

Otago Witness, Issue 4057, 15 December 1931, Page 24

NUTS TO CRACK

By

T. L. Briton.

(For tue Otago Witness.) i Headers with a little ingenuity will 1 find In this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of th. " nuts " may appear harder than others, it will be found that none will require a sledge-hammer to crack them. Solutions will appear In our next Issue, together with some fresh " nuts." Readers are requested not to send In their solutions unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. FOUR TRADERS. Four traders called J, K, L, M respectively, who had been doing business with one another during a period of some months without comparing accounts, decided to have a settlement. Each placed his money on the table in front .of him, this being the only cash held by the four. K had £lOO more than J before starting to settle, but the comparative sums held by the others are not known. The first transaction was the payment of' K’s debt to L, which took one quarter of the total sum that K- had brought with him. The total amount then held by K and M together was equal to the combined sum that the other two had. M then paid his debts to L and this took exactly one-third of his money. One quarter of the sum that L then held was the amount that he paid over to K in settlement of the debt between them, and the latter squared matters with J by handing over to that dealer one-fifth of the money he then had. z\t this juncture L owed the other three traders £5O each, and after paying them he found that it took from him exactly onequarter of the sum that he was holding before handing the money over. The question is how much did each have at the start if at the conclusion every one went away with equal sums? A FRONTAGE FENCE. “ Devotee ” sends the following question, which, though an elementary one, may interest the reader: —Two men had a contract to erect a palisading fence along the frontage of a school ground, the length of 420 feet. The specifications showed that the panels were only to be three feet in length, and the men, starting at different ends of the line, each took with him half the number of posts that was considered sufficient for the work, namely, 70 each. They followed the line as marked by the building surveyor, and each man erected his posts three feet apart as required by the specifications, but when each had erected his 70 posts it was found that there was a gap of six feet between the two posts last erected. While they were arguing the point, each blaming the other for not observing the proper distance as mentioned, the school master came along and explained the matter to the men. What mistake had the men made? The correspondent (evidently a very precise person) states, “ Width of posts may be ignored,” and to this may be added — also the class of timber used. THE FAMILY DOG. Ludham and his wife usually take walks together before dinner in the evening, and as the suburb is generally free of heavy traffic at that time, the dog usually accompanies them. On one occasion madame started from the front gate alone, her husband being engaged

with a caller, and the dog remained with his master. She left the gate precisely at half-past 5 o'clock, and after she had strolled for half an hour at a uniform rate along the perfectly straight footpath, Ludham and the dog left the gate to catch up to her. As soon as released from the gate the dog bounded along to his mistress, and, without delay, raced back to his master, who had continued to walk at his usual speed to overtake her. The dog continued racing backwards and forwards in the manner stated without stopping until Ludham overtook his wife, who had not varied her speed from the starting-point, her leisurely rate being one mile per hour. Here is an interesting question upon these facts for the reader to answer: If the respective rates of travelling of man and dog were two and five miles per hour throughout, how far had the dog run by the time that Ludham reached his wife? When the reader has read this carefully, he will readily see how absurdly simple is the arithmetic of it, for there is no necessity to trouble about the distance walked by the two people. PROMISED GOLF CLUBS. The only daughter was continually asking her mother to buy her a set of golf clubs, and was as often told that these were not made in children’s sizes. Upon the last occasion that the mother was importuned in this way, the daughter was told that as soon as her age was equivalent to two-fifths of the mother’s, the promised clubs would be purchased. As the youngster was then only of the average Standard V age she realised that there would be a wait of some years before her wish were satisfied, but how many she could not say. No doubt the reader will be able to tell, whilst sitting in his armchair, if given the following additional information:— If, when the daughter was exactly half

as old as she is now, her age was onefifth that of her mother’s at that time, and one-sixth of what the latter’s age is now, how long must the youngster wait before the time arrives for the purchase of the promised clubs? The respective ages of the two people are such that the daughter’s years were at one time equivalent to one-seventh, and later to one-fifth of those of her mother, without odd months entering into the calculations, and in due course her age will be, in an even number of years without fractions, exactly two-fifths that of the mother, the reader being aware that such positions cannot occur twice in any two person’s lives. TRANSIENT GUESTS. The vestibule of a city hotel had an unexpected influx of guests from the country recently, and some of the details will form the material for a useful little problem. When the proprietor saw that not one of the visitors had booked for more than dinner, bed, and breakfast, and that only 10 out of the large number required the whole three services, he remarked that the popularity of the motor car had effectively put an end to the old custom of people spending more than one day in the city whether on business or pleasure bent. Some of the visitors booked only for one of the three services, whilst a larger number required two only of the three mentioned. One-half the total bookings had dinner, two-thirds had sleeping accommodation, whilst one-half of them had breakfast, these proportions indicating that, besides the 10 who booked for the three services, a good number had bed and breakfast, though only one-fifth of the entire bookings were for breakfast only. From these few details can the reader find how many visitors booked for either one or more of the three services, including, of course, the 10 who secured all three?

SOLUTIONS OF LAST WEEK’S PROBLEMS. AN OIL WELL. As £3OOO represented one-third share Adam’s portion is £5400 and Brown’s £3600 of the full value before selling the third share, and the latter would receive the difference between £3OOO and the value of his interest, which is £6OO. The balance of “ C’s ” £3OOO should therefore go to Adams. NO FREE LIST. One thousand four hundred at 9d, 500 at 18d, and 100 at 2s 3d. DISCOUNT FOR CASH. Twenty-four shillings per dozen, with 3 per cent, off marked price for cash. A SLOW RUN RACE. The plank was six feet in length. DOWN IN A VALLEY. It applies to any place, for the sun at the horizon is 4000 miles further away from any place on the earth than it is at noon, that distance being one-half of the earth’s diameter. So the 1000 mile deep valley is “ well within the mark.” ANSWERS TO CORRESPONDENTS. “ Measure.”—Measures of length in France are based on the metre, and all other measures are got either by subdividing or multiplying the metre by 10, the French system being entirely decimal in character. “ Curious.”—Your comment and continued interest are appreciated.