INTELLECT SHARPENERS

Otago Daily Times, Issue 21266, 21 February 1931, Page 21

INTELLECT SHARPENERS

Written for the Otago Daily Time*. By T. L. Bstwk. THREE STOCK DEALERS. Three stockdealers, who may be called i* x,” “ Y,” and “ Z ” respectively, yarded & number of sheep for sale, the animals comprising ewes, wethers, hoggets, and flock rams. Each dealer had his own mixed lot. Discussing on the evening before the sale what the market was likely to be, they made among themselves some exchanges of their stock, which gives rise to an interesting little problem, viz., to find from the apparently meagre data available, the number of sheep each man yarded. The details are based on three different suppositions. First, if “ X ” exchanged with “ Y ” five hoggets for one flock ram, the positions would be reversed so far as concerns the number of animals each of those two dealers then bad. Second, if “Z ” gave “X” 13 wethers for one ram, the latter owner would have exactly three times as many sheep as “ Z.” Finally, if. Z exchanged with “Y” seven ewes for one ram, those two dealers would then each have an equal number of animals. When the reader is asked to find how many sheep each man had before the bartering took place, he will note that three distinct transactions are assumed. AN INGENIOUS PUZZLE. A correspondent “ Philately ” has sent r very interesting puzzle of an everydav ” variety (not his own he says) concerning postage stamps. Upon being looked into it is found to be almost identical with one forwarded by a reader, O.W.C. some considerable time ago for publication in this column. The solution of the puzzle is ingenious, and if the wouldbe solver is unaware of the method, he should not _bcgrudge_ 10 minutes, or even more, of his spare time in an effort to unravel it. Twenty-five stamps are in an unbroken single strip, perforated in the orthodox manner, and without any selvedge. The puzzle is to separate this strip into 25 separate stamps in the fewest possible number of “ cuts.” “ Philately ” states that he does not know anyone who is able to accomplish this in jfewer than five “ cuts,” but perhaps some reader will find a shorter method of doing it. In fact, O.W.C. has a plan of performing the feat much more quickly, judged by the number of “ cuts ” which he. finds necessary. AT £IOO PER ANNUM. Here is another example of those curious arithmetical paradoxes that not infrequently trip one. It is somewhat of the same character as the two typiste problem which appeared in this column. A and B are two clerks who start at a salary of £IOO per annum each. The former receives a rise in wages at the rate of £2O every year, while B’s income is increased by £5 every half-year, their salaries being paid half-yearly. The question is not, as was the case concerning the two stenographers, which one received the largest sum by the end of a given period, but which clerk had the largest income received in this manner. The reader will of course not require the aid of pen or pencil to enable him to reach the proper conclusion, though, to convince his doubting friend, either may be necessary. IN A’CHURCH. Mr W. R. Ball, a London mathematician, is the author of this little problem, which occurred to him whilst seated in his seat prior to the commencement of a church service. The hymn board in the church has four horizontal rows in which the numbers of four hymns chosen for the service are placed. The hymn-book in use from which the numbers are taken contains exactly seven hundred (700) hymns, and Mr Ball’s interesting question is, What is the smallest number of plates or cards, each containing a digit, which must be kept on hand so that any four different hymns can be displayed on the board? And how would the result be affected if an inverted six can be made use of as a nine (9)? After the reader has found the correct answers to these two questions, perhaps he may feel disposed to calculate how many cards would be necessary, under- similar conditions, where five hymns are chosen for the service as is the case in many New Zealand churches ? WINE AND WATER. Here is another question of quite a simple character which may for a moment or two not be obvious to the reader, for not infrequently incorrect answers have been given to it by persons ■who certainly should not have been caught napping. One glass is half full of water, and another is half full of wine. From the latter tumbler a teaspoonful of wine is taken and poured into the glass containing the water, and the same spoon is then used for the purpose of transferring a teaspoonful of the mixture of wine and water to the glass of pure wine. As the result of this double operation is the quantity of wine removed in the first operation greater or less than the quantity of water in the teaspoonful of mixture taken from the other tumbler? Simple as this question apparently is, the reader will perhaps agree that the correct answer may not be what seems at first thought, and quite a number of people cannot agree with the correct answer. It may be mentioned that the tumblers are the same size, should the reader raise the question. LAST WEEK’S SOLUTIONS. TWO COGGED-WHEELS. They would come together 25,000 times in the time stated. ONE FOR THE ARMCHAIR. It would take 13 minutes to travel the distance mentioned. BETWEEN THEMSELVES. X had four halfcrowns, four florins, and two sixpences at the start; Y had two halfcrowns, four florins, two shilings and two sixpences; Z had two florins, four shillings, and four sixpences. As X lost five shillings and Y one shilling both to Z, the reader will be able to find what actual coins were exchanged, so that each person had 10 at the finish. CHANGE IN SILVER. Four coins would be necessary as the difference is 5s 9d. A person could hold 15s 9d in silver without being able to give the exact change for a 10shilling note, and £1 5s 9d in the case of a'sovereign. A COAL MERCHANT. The sum spent was £B4. ANSWERS TO CORRESPONDENTS. L. E. W. —Thanks, will be looked into as it seems somewhat off the beaten “Periphery.” —Yes, there was a condition omitted which rendered the statement obviously incorrect. (2) If a rectangle, the closer the figure apporaches the shape of a squaie, the larger the area will of course be. « Singapore.”—Measures of weight, viz., “Picul” and “Kati” (Chinese) equal to one hundred and thirtythree and a third pounds,, and one an da third pounds respectively, are in use in the Straits Settlement, but measures of length and area are the British system.