INTELLECT SHARPENERS

New Zealand Herald, Volume LXXI, Issue 21396, 20 October 1934, Page 5 (Supplement)

INTELLECT SHARPENERS

By C. J. WHEREFORE

SUNDAY AFTERNOON Mr. David and Mr. Jonathan were in the habit of going for a short walk together over the same route every Sunday afternoon. The distance scaled on a map was a whole number of miles without fractions, and they were able to make it keep them always one hour away from their homes. Now these two friends have cars, and they seldom walk at all. One of these ears can be driven at a speed of six miles an hour more rapidly than the other, and when they drive over the route of their former Sunday walk, this car takes exactly one minute less than the other one on the journey. These two velocities are also whole numbers of miles without fractions. The problem is to discover what they are. BIRTHDAY PRESENTS Mrs. Needy's wealthy brother was staying with her for a few days. It was fifteen years since the last time he paid her a visit. Her youngest child, Amy, had a birthday, and the uncle, feeling that he had not been doing his duty in the matter of birthday presents lately, made this a pretext for giving each of his nieces a cheque for the same amount. In the case of Amy the amount was equivalent to a pound for every year of her age, but the total paid to Bessie and Clara amounted to only 12s 6d for each year of their combined ages. The eldest girl, Clara, is the only one of the family whom he had seen before this visit, and he might have celebrated her birthday instead of Amy's if he had arrived a month later. If he had then chosen to give the same presents as he now gave, the sum received by Clara would have been half as much for each year of her age as the amount for each year now given to Amy. What are ages of the three girls, and how much did their uncle give them ? PUZZLE IN WORDS Five men, all interested in the peculiarities of certain words, were discussing their favourite subject. Each one had found a word of three syllables which could be changed into another word by altering one letter not far from the middle. The first man said that his word was an adjective, meaning something not unlike early, but the change of one letter made it into a term signifying value. The second said his word was also an adjective, and it implied finality rather than early occurrence, but the change of one letter made it into a laughing matteri The third man said his word described an injury, and could be, changed into a disorderly state. The fourth said his word was one which would be found in a work on physics, but after altering one letter it meant merely drawing something back again.. The fifth said his word meant rather drawing things together, and could be changed into a word implying building up. Can readers find these words? ARMCHAIR PROBLEM Two men accepted a contract to dig a ditch for £l2. A third man, who had been without employment _ for some j time, asked permission to join them,

and was offered ten shillings a day. He refused this, so the agreement made was that each man should dig at a • different part of the line, and that, their separate contributions should be measured and paid for in proportion to the fractions of the whole length which each man had dug by himself. The work was found to be more troublesome than expected, and the result was the three men took eight days to;' finish the contract. They found that one of the two original men could havedug the whole ditch in 20 days and the other in 16 days. The question is to what extent did the third man pro- , fit by refusing the offer of ten shilling# a day? GEOMETRICAL PUZZLE A ladder, Sft. 3in. in length,/' stands on level ground and leans against a perpendicular wall, which it, touches at a point- 7ft. 3in. above the ground. Is there room for a box, which is a 30in. cube, to pass under this ladder when one surface of the cube, rests on the ground? The answer is: readily found by drawing the objects I described to scale, but can readers dis-. cover a simple arithmetical solution?, 1 POSTMASTER'S PROBLEM " We had a very strenuous after-, noon," said a postmaster. " A large number of persons are taking part in a competition, in which each', participant has to send sixpence worth of stamps with his entry. Shortly before closing time the supply of stamps wasi so short that we had to make up the sixpence worth in every way it is possible to do so." His friend naked whati values of stamps were kep:; in stock, and to this he replied readily that these included every multiple of a penny and also stamps at £d, ljd, and 2}d. But in reply to another question, namely in how many ways he had found it possible to supply sixpence worth, he was more reticent. Readers have now th»' chance to .discover this themselves. Last Week's Solutions Catching the Mail.—Half mile. Anagram.—Grandee, enraged, derange, angered, grenade. Erratic Watch Problem.—He should wind it and set hands at 11 a.m. This is a good specimen of the kind of problem which can be worked out by a graphical solution. Girl's Day in due is that the bus fare could not be paid with 1 less than three coins, but two-thirds of it could be paid with one. It was 3s 9d, and the cheque was for £5. Result ol a Breakdown. —To solv© this problem we have to discover whether she gave him sixpence worth or ninepenec worth. Actual trial shows it must have been the larger value, and thus there were 21 passengers!, of whom 13 paid ninepence and 8 paid sixpence. . V Armchair Problems. pounds. (2), 42, 39, 14, and 13 years. (3) The charge for admission could hardly be otherwise than sixpence. Therefore, 6 must appear in the "pence columns, so that the sums paid were £1 5s 6d and £2 4s 6d, for 51 and for 89 children-. .