INTELLECT SHARPENERS

Otago Daily Times, Issue 22911, 19 June 1936, Page 20

INTELLECT SHARPENERS

Written for the Otago Daily Times, By C. J. Wueuefoue.

[Correspondence should _be addressed to Box' 1177, Welliugton.J

ARMCHAIR PROBLEM. "It used to take between eight and nine hours on the road, when I went to town by the coach in those days,” said Mr Oldman. “We used to stop for dinner ami change horses at the Crown Hotel, which is three miles beyond the hallway point of the journey. Now my grandson can drive me the whole way in his car, which travels six times as far as the coach, and wo pass that obsolete hotel, doing so many miles per hour, and only three-quarters of an hour after leaving here.” Mr 0. mentioned the speed at which the car is driven, but for the purpose of the problem this is omitted. It is to be understood that no fractious of miles are used, and the question is, how tar from town is Mr O.’s residence?

THREE ANAGRAMS. In the lines given below the first two spaces arc to be filled with words composed of the same five letters. The third and fourth words are also composed of five similar letters and the fifth and sixth of six similar letters. “ Within this a prisoner am I,” She it in her desolate abode, And when some knight of fame and comes by, She means to her missive on the road. But champions don't to pass that way, So there she must for many a day.

A WORKING AGREEMENT. Mr N. Driver is not a supporter of the 40-hour week, but he has some obscure theories about rationing his work among those whom he employs. His method is to engage a man at a certain amount per day; then on each successive day the pay is made less by a certain fixed amount, until it becomes so unprofitable that the man departs and another works in his place. For example, if a man were cm gaged at eight shillings on Monday, lie might receive only seven shillings on Tuesday, six ou Wednesday, and so on. These figures arc given as examples only. The pay for the first day, he says, is 16 shillings, but he did not inform me how much he deducts on each of the following days. But he thinks the men must be consulting some mathematical adviser, because everyone continues to work for just 10 days, and the result is that the cheque be receives is the maximum obtainable under this agreement. By how much per day does he reduce the daily payment?

DEFERRED PAYMENTS. “Do you want another problem?" was the question asked, and when I had replied, my friend went on. “Very well, one of my relatives was anxious to buy a clock, but, as usual, she had not quite enough money for the one she wanted. The proprietor of the shop was willing to let her have it for a deposit and an undertaking to pay the remainder at the rate of half a crown per week, and did not increase his price for the concession thus made. But the purchaser had to suggest a smaller sum —namely, threequarters of what was asked, and the man, who was really keen to do business, agreed to her proposal, again without adding to his price. The amount paid weekly was only two shillings, but she paid this for eight weeks more than the time originally proposed.” “ I suppose you want me to guess the price and the number of weeks allowed for paying it?" I remarked. “ Isn’t there rather a liberal number of possible solutions?" “Oh, no,” was the reply, “ the price is quite certain, and the number of weeks also, if you take my word that they agreed to cut it down as small ns possible." Was she correct in saying so?

A VERY OLD PROBLEM. A book, which the present writer has been privileged to borrow, gives some interesting details about the mathematical ability of the ancient Egyptians, about JBUU to 17(H), Ji.C. The persons ret erred to were public servants, who had to attend to the keeping of the calendar, a systematic one of 305 days, and advise the population of the arrival of the dates for ploughing, sowing and other such operations. They also designed granaries, and entered into calculations about the amount of grain which could be stored in buildings of various shapes aud sizes. It seems only natural that such authorities should seek some mathematical recreations, and this is one of their invention! In each of seven houses there are seven eats, and each of these cats kills seven mice. Each of these mice, if it had survived, would have eaten seven measures of grain, and each _ measure of grain would make seven units of bread. How many units of bread have been saved by these cats? Of course, the answer is the fifth power of seven. It is interesting to notice that these problemists were able to perform multiplication of figures, which amount to thousands, because they had not the advantage of modern numerical notation, in which units, tens, and hundreds are distinguished by writing them in position. A probable theory is that they used beads or counters, but this will not explain bow they could handle fractions, and the following exercise cannot be worked out without them. It is given here in the usual way, as it seems quite good enough to be a sharpener of present-day intellects. Divide ten measures of barley among ten men, so that each one in his turn shall received one-eighth of a share more than that given to the man before him.

SOLUTIONS OF LAST WEEK’S PROBLEMS. W ord Change.—Keen, seen, seed, feed, feel, fuel, full, dull. Promise.—Joan’s bicycle must have been much the best of the three. It cost £l2, and the others cost £4 and £2. Complete Cure—The factor is increased by I every three years, therefore the ratio 14 to 1 comes into effect in 30 years. Ages.—The two factors are one more and one Iqss than 0. so that Miss C’s age is 35, and that of her sister is 30. The interesting point is that this solution is obtained without knowing how many handkerchiefs were bought or how much was paid for them, , Substitution. —It is not possible to pet every letter, and more than one solution may bo found, but none of them seems to fail to give some of the letters required. The best result scorns to bo 2380 plus 2970 equals 5350, from which it follows that the first six letter,* are UNI FOB, and the last is obviously M. Armchair Problem.—Every day one man caught five and the other seven. But they have to maintain this ratio, so that the only possible method of exaggeration is to double the numbers. Therefore they really caught 49 aud 35, and they say that they caught 98 and 70.