INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVI, Issue 20152, 12 January 1929, Page 5 (Supplement)

INTELLECT SHARPENERS.

UNCLE AND NEPHEW. B¥ T. U BRITON. A man who was given to speaking enigmatically was remarking to some friends upon tho excellence of an operatic performance he had witnessed. He said that his uncle and nephew accompanied him to tho theatro and that he had purchased tho tickets for tho party. JIo tendered a £5 note at tho box office and received tho required tickets together with £3 10s change. Now hero comes the enigma. Tho man stated further that tho change mentioned was right, though tho tickets cost fifteen shillings each, adding that tho number and value of tho tickets wero also correct and this, the ticket clerk confirmed. Can tho reader say how this could bo possible, in view of the fact that nono of tho party was on tho frco list, full prices being paid for each. THREE TIME-PIECES. In a certain government department there wero threo clocks, nono of which could L>o relied upon for tho correct time.Ono gained uniformly ten minutes a week, another gained fifteen minutes in the samo time, while the third lost regularly at the rate of five minutes a week. That was their record when tested, and tho expert who was called in to udjust them first allowed tho thrco clocks to run on, each at its own uniform rate mentioned until tho three time-pieces showed tho samo time. Supposing that at noon to-day, Saturday, January 12, the hands of tho clocks showed twelve o'clock together and were allowed to run on at tho respective rates described, can the reader say ivl*ri tho three time-pieces will first show identical time again? To obviato any possible confusion in writing a.m. and p.m. tho reader may adopt the practice now in vogue of writing the hours as from ono to twenty-four o'clock, for example, 1 p.m. would in this way bo 13 o'clock and so on. WHAT TIME WAS IT 7 A very simplo cvery-day question is prompted by tho previous problem. Before stating it, however, tho reader will quite understand that in calculating problems concerning measures of time, ifc does not necessarily follow that the correct solutions can always bo indicated- on the dial, for somo results may involve fractions of seconds which no ordinary chronometer can show. The following problem, however, will require a solution only to the nearest half minute, ignoring odd seconds and fractions. Upon looking at my watch between four and fivo o'clock one day, and again between eight and nine o'clock it was noted that the hands had exactly changed places. Now, by examining a dial it would be easy to demonstrate to a minute or so the exact time that I looked at the watch, but can the reader make the necessary calculations and find to a half-minute what those times were ? The arithmetical process is quite a simple one. MADEIEA WINE. A wine taster blended a " Madeira "• from four grades of wine under instructions that the mixture should be worth 17s 6d a gallon, based upon the quantity, and value of the four wines comprising it, which may be designated A, B, C, and D. The values were all .different, the highest being A grade, the, prices descending to the inferior class D. The taster mixed one gallon of A with three gallons of D, and one gallon of C grade with two gallons of B, putting the whole into one keg. In this way the blended wine was worth 17s 6d a gallon based on the individual prices; A and B being each priced more than this sum per gallon, while C and D were each of lower value than 17s 6d. Can tho reader crack this little nut, and find what was the price of each grade ? IN ALPHABETICAL ORDER.

Ingenuity rather than theoretical knowledge will be required to solve tho following puzzle. Arrange the first 24 letters of the alphabet in the following order of four rows with six letters in each, and then find out the fewest number of exchanges required to place them in alphabetical order. This problem will require much thought before it can be solved in fewer than eighteen moves, for although two letters are already in their proper places, and the first three moves, A, B. and C are obvious, a little difficulty will no doubt be experienced before achieving the correct result. An " exchange " is merely transferring one letter and putting another in its place, and there is no lfifiit to the number of times any letter may bo moved. OAB O H U Q F R X L> .T MIP D T E SGW N V K If any reader should accomplish this in 17 moves it will be (in tho writer's opinion) the fewest possible, though it is claimed to have been done in. 16 exchanges. LAST WEEK'S SOLUTIONS. Mathematical Letter Sorter. The number of tho house to which the letter was addressed was 35, there being 49 houses on that side of the street. A Possible Error. The number to bo multiplied by 106 is 22, the product being 23,532. By placing the figures in tho wrong, positions as described but otherwise correctly multiplying, the product would be *3552, or 19,980 less than the correct result.' Coincidences at Cricket. Y team scored. 128 and 72, and X 96 and 54 runs, the former thus winning by 50 runs. Two Armchair Questions. (1) Half a pint of water was added to each quart. (2) Under the conditions 156 apples could be purchased for tha sum named. Eureka. One method is as follows:—12 to ©, 7 to r, 10 to E, 8 to A, 9 to U, and Uj to k. _______________, ANSWERS TO CORRESPONDENTS. " School."—Yes,' it could be treated as a " quadratic, " but why " fly so high " when simple arithmetic 'supplies the process '! "Caught Out."—Yes, the average would bo as you say. " Avoirdopois. "—Add the ten weights and divido by the difference of the highest and lowest.. •„ :• " Appreciated."—-The theoretical result in any case is always determined by the relationship between ono of the, two movable objects and the other. It is a very useful formula to know.