INTELLECT SHARPENERS

New Zealand Herald, Volume LXXIII, Issue 22332, 1 February 1936, Page 5 (Supplement)

INTELLECT SHARPENERS

■ ANNUAL LEAVE " How many months have there been since your last holiday?" asked the Direct Questioner. The Evasive Answerer told him that their number was one less than the number of days he was now permitted to be absent. " At that rate," said the first speaker, " if you had been kept waiting for another three months., would you have claimed three days more?" Certainly I should, if it were calculated to fractions of days, I should be. entitled to three days more and one-fifth of a day after that.'* How long ago was Jus last holii day, and how many days' leave have been granted to him now? ARRIVAL OF THE MAIL Beryl says to Alice: " You have as many letters to-day as Cora and I have together." Cora says; " Beryl and I have tho same number to-day, and yesterday she had only one more than I have.'' Alice says to both her sisters: "The day before yesterday I had the same number that both of you have to-day, but you, Beryl, had one more, and Cora had two more." Cora.'s last word is: "Yesterday Alice had the largest number any one of us has had on one day," Their mother stops the argument with the remark that on each of the three days mentioned the totals reoeived by the girls were the same. How many letters did each of the girls receive on each or the three days? THE CHILDREN'S PAGE A correspondent inquires about the following puzzle, which, he says, was published in a page for children. He wishes to know whether it is a fair question to be set before boys and girls. A man bought one goose, two fowls and three ducks for £4. The price of the two fowls and three ducks was the same as that of three geese, and the three ducks cost as much as the two fowls. What did each bird cost ? Perhaps it is the simplicity of the problem which makes it difficult, if that quotation is not already overworked, beoause the numbers are repeated so obviously, that they should catch any eyes, youthful or adult, and show that the £4 was paid for the equivalent of the value of four geese, If tho children discovered no more than that they do not deserve especially high marks for doing so. Here is a better problem from the same material, and children are not to bo Intimidated into tackling it, unless they really wish to. Let the prices bo £l, 15s, and 10s, as before, then try to find what are the Ihrgest arid smallest numbers, which can be bought for £lO. if it is agreed that birds of all three descriptions must be included. SEVERAL IMPROBABILITIES " The children came homo from school to-day very pleased with themselves," said Airs. Farmer, while laying the table for tea. " They say thq master set them a problem, which he took out of a newspaper, about Belling fowls, ducks and geese, and everyone in the school solved it, althoiigh they took quite different lengths of time to do bo. Those who found tho answer mos? quickly wero given tho lughest marks, (

By C J. WHEREFORE

and Ruth got SO more than Tom. In fact the aum of the squares of the numbers of marks received by Tom Jmd Stanley were only just equal to the square of the number of Ruth's marks., How many do you think they got?" " That is easy, said her husband. Is it? IT SEEMS EAST " I have another problem for you," said my helpful friend, "There were two stalls at a bazaar, each of wliich offered all articles on it at the ; same price, but one of them charged one shilling more than the other. Three gjirls came there with a pound, which had been given to them by their father to be spent, Mercy bought several articles at the cheaper stall, then Charity bought two-thirds of Mercy's number at the same stall. They gave all the money that was left to' Prudence, and it wa3 just enough to pay for four articles at the other stall." 1 "That looks easy," I replied. " The two girls sE«nt six and four shillings at an 18-pe;any stall, and the third ono spent 10 shillings on half-crown articles. But you should have said that the second girl spent two-thirds pf the sum spent by her sister." At this point my friend assured roe that I was wrong from beginning to end. She said she meant just what she said, and that I could not take two-thirds of four to solve her problem, nor for any other reanon. It was evident that this would require some hard thinking, and I asked whether the girls had agreed to spend only silver/without pence." There you are off the fails again," she replied. " Only one girl spent shillings without pence, and I am not going to tell you which one it was." How many articles were bought at each stall, and what were the prices paid for them? LAST WEEK'S SOLUTIONS Payment by Instalment?.—-The oasK price was £6. , Three Mobs of Sheep.—No, it is nob sufficient, because if therd were 700 sheep he must have been speaking to A, or if there were only 600 he was speaking to B. Four Daughters,—A is evident!;? a girl at school, and B s|>eaks of her mother's house as home. .D's first idea about a car is that she and her mother can share it. Therefore these three are eliminated and C must bo tho married daughter. Armchair Problems- —(1) The :suifc cost either three ;p:uineas or seven guineas, and as it was made to measure evidently the higher price is the correct ono. (2) The four pence saved is one-fifth of the price of lib- or coffee. Therefore the coffee cost and the tea cost 3s 6d. (3) Eigbt nmes, because it is clear that he rode back sn one hour. A Small Estate .--Add the 632 and 466 to the 995, and divide by 3. lh# quotient, 661, has no factors, and muse be the mother's share. From * rtb-, tract 456, the remainder, 205, is duct of 41 and 5, and has no factors, therefore there were ! dren of one sex, each of whom r»w. £4l. The other remainder, duot of 43 and 3, therefore the** three children of tha pjs