INTELLECT SHARPENERS

New Zealand Herald, Volume LXXIII, Issue 22350, 22 February 1936, Page 31 (Supplement)

INTELLECT SHARPENERS

HOLIDAY CLOTHES

When Mr. Shingle came to town for a holiday, after several months in the back country, he felt the need of some new clothes. A few hours after his arrival he caine to his hotel wearing suit, hat, and tie, which were all very obviously newly bought. In evading some rather personal questions, he told his friends that the suit had cost him eight shillings more than an exact number of pounds. The price of the hat ended, with eightpence, and that of the tie with sixpence. If the price of the suit were diminished by one shilling, it would be just three times as much as that of the hat. And if the price of the hat were increased sufficiently to make it shillings without pence it would be 16 times the price of the tie. How much did he pay for each of these three articles P WORD CHANGE In the lines given below the spaces are to be filled with a series of words, each of which differs from the one before it by one letter, making the last word quite unlike the first and with exactly the contrary meaning. His words were far from , his was vexed, His car behaved like——, and would not start, Which made his thoughts more heated and perplexed, As may .warm and influence the heart. A friend of experience bade him stay, And his temper with a tighter rein, He answered in a y- unfriendly way, And got what he did not deserve, you'll say, For then the engine started off again. TWO CYCLISTS Two boys bought a bicycle, and on every day for a week each of them rode it for a few hours. There was a cyclometer on it, each of them read it carefully, with the result that they found they had ridden on each day three miles more than on the preceding day, This was quite true, but the cyclometer was a cheap and unreliable article, and when the full extent of its error was ascertained it was found that the total nuinber of miles on each of these days was one less than they had supposed. They had mentioned the first result to an elder brother at the university, who pointed out that the total for the week was a perfect square. When they had to inform him of the error, thoy also told him how many miles each of them had accomplished. To this he replied that the new figure was not less interesting, because it meant that the numbers of miles ridden by each boy were cubes. How many miles had they ridden really, and hoV many did they at first think they had ridden? ARMCHAIR PROBLEM Mrs. Smith owed Mrs. Jones eightpence. They made a visit to town one Friday evening, for the purpose of obtaining some fruit for making jam, and Mrs. Jones paid both tram fares. They had tea together, and Mrs. Smith paid the bill for both, the price being tlireo times the amount of the tram fare. They found it cheaper to buy a whole case of fruit, and agreed to divide it eaually. but as this was a considerable outlay of monev, each of them paid her own share. After this they returned to their homes feeling contented with their shopping, and also re-

By C. J. WHEREFORE

lieved when they found that the debt mentioned above was now repaid. What were the charges s£>r tram fare and for tea? SELLINGS A FARM " Yes, I have brought you another problem, and quite a good one," said my informant, at the same time opening her note book, and searching for some page required. "It'is about a farmer aijd a stock and station agent,who were taking a prospective buyer over the farm." She had to consult her notes here, and I asked whether the farmer or the agent for the mortgagee was selling the property, as it might make a at any rate to the farmer. She replied that her problem was rifther complicated, and she would have to read it to me, especially as my interpolated remarks were not particularly helpful. " The buyer asked how many sheep there were, and the alleged owner of them replied that there were 300. The agent said they were worth £3OO, although there were - three varieties of them, valued at 30, 25, and 11 shillings per head. They came to paddock A, and the questions led to the fact that there were 100 sheep of all three kinds, and their value was £IOO. The same information was given in paddocks B, and C, with the warning that the numbers of sheep of the three varieties specified were quite different in each of the three paddocks, although the mobs in each of them were always worth £100." 1 asked her whether the nine numbers were all different, and this time she bent her head over her notes for some time before replying. " I see that one number does occur twice, the tallies of two differently priced lots in two different paddocks. I suppose that makes the problem more difficult, doesn't it?" How many of each kind were there in each paddock, and does the detail about the repeated number make the problem more difficult or more simple P SOLUTIONS TO PROBLEMS Armchair Problem.—To make the difference a minimum the tickets must have cost 9s 7d and 9s sd, making the differenco only twopfence. Photographer's Problem.—lt is clear that the shillings column must have shown aO. The answer is 19 copies at 3s 2d, costing £3 0s 2d. The Number ol This Year.—(l) The next is 2048, which is the eleventh power of 2.(2) 1937 is the sum of the squares of 41 and 16, and is admissible in this manner, although not in the other way. Problem In Ages.—A and B must be of the same age, both 0, otherwise there is no solution. C's age to <25,, Jhe numbers in the boxes are 15, 16, and " 69, and the problem can not be solved without discovering these numbers als£. Borrower and Creditor.—The weekly allowances are evidently sixpence and ono penny. It follows that the sister's loan must be a multiplo of elevenpence and 44, is the only one that will fit. Therefore O and E contributed; eightpence and four shillings respectively. Sporting Information. —J and N say Locksloy was first. If this is not true Cedrio was both third and fourth, therefore it is true. M said Locksley ivas second, and, as this is untrue, her other statement that Athelstane was third is correct. Then we can see that K spoke untruthfully in saying'that Athelstane was fourth, so it is. true that Cedric is second. Also Leslie «4id untruthfully that Cedric was fifth, it is true that Rowena was fqurtp« it follows thct pieJTriar, which,sr**?father baoked is fifth.