INTELLECT SHARPENERS

Otago Daily Times, Issue 21951, 12 May 1933, Page 2

INTELLECT SHARPENERS

(Written for the Otago Daily Times.) By T. L. Bmton. ATHLETIC CONTESTS. Two athletes, Brown and Jones, engaged in two competitive events, the first being a two mile race, which was won by Jones. The other was a walking contest over a longer distance, and on the details of these two incidents two useful arithmetical puzzles are presented for the benefit of the reader who enjoys the solving of these simple puzzles. Had Brown in the first contest run one-third faster than he did, he would* have won the race by 22 yards instead of losing it. What were the respective speeds of the two athletes?

Though both men took the same route in the other event, Brown started some time before his adversary, and jogged along at the. easy gait of 100 chains per hour until Jones caught up to him. The latter started from the same point as Brown, but some time afterwards, travelling at the rate of 1J miles per hour, he overtook the latter walker at the end of six hours and 40 minutes calculated from the time that the faster man started. The pace of both men was what is known as go-as-you please," and though at some parte of the journey each man travelled at five miles per hour, both rested by the way, making their average rates of travelling as stated. In asking the reader how much start Brown had from Jones, he will, of course, not require either pen or pencil to find it. SEVEN SUBSCRIBERS. Here is a little puzzle which demands the simplest of calculations, and, as the figures used in the statement of it have been chosen in order to avoid difficulty, the question may well be treated as purely one for the armchair. Six gentlemen agreed with a seventh to provide a certain sum of money to a deserving cause under the following terms arranged mutually:—The first six should each subscribe £IOO to the fund provided that the other donor gave £2O more than the average subscribed by the whole seven benefactors. This was consented to by the seventh, and the question is how much would the organisation receive as a joint subscription under these conditions, and how much more than each of the subscribers of £IOO, did the seventh gentleman give? It will be observed, of course, that the £2O mentioned in excess of the average of the seven subscribers must be included in the gross sum when the average is being calculated.

TWO ARITHMETICAL PUZZLES. Both for the armchair. Two clocks pointed to 2 o'clock at the same instant on the afternoon of last New Year's Day. One of these timepieces loses seven seconds consistently every 24 hours, and the other clock gains eignt seconds regularly in the same period. . At these respective rates can the reader eay at what time of the day and on what day after New Year's Day when the clocks started to lose and gain in the manner stated, will the hands of one clock show the time exactly one-half hour ahead of the other, and what times respectively will the clocks show then? A man bought an article and sold it at a profit of three shillings. Upon calculating this profit he found that if the percentage of profit were estimated upon cost price, as is the correct method, the percentage would be one-quarter as much again as it would be it the profit of three shillings were reckoned as a percentage on the selling price, as is the practice in/ some commercial houses. Can the reader say how much the article cost? WITHOUT PEN OR PENCIL. In response to many requests from readers, the percentage of puzzles for the armchair has been increased in recent days, and as one does not care to move from the fireside .at this time of, year, would-be solvers will be accommodated m this way, aud will find ample material for the exercise of their mental faculties without bothering with pen or pencil. Of course, this column caters for a large circle that enjoys problems requiring more serious thought, but the armchair variety of puzzle will always be found in a generous proportion every week. The age of a husband to that of his wife is as four to three, and 24 years ago the ratio was four to two. What are their respective ages? . . The sum of 20 shillings was divided between 10 boys, 8 girls, and 11 smaller children. Each boy received twice as much as a girl, and every fou r girls as much as seven of the tiny tote. .Wftat share of the pound did each child m tne three groups receive? . A grocer bought eggs at a certain price per score and sold them at threefifths of that price per dozen. If tie bought - two pounds' worth at the price stated and sold them all at the selling rate mentioned how much profit aid ne make in the transaction? A PUZZLING CODE. ' Here is a passage in code that may, and probably will, provide the would-be solver with half an hour of serious thinking and possibly test his ingenuity to the full. It is based upon a plan which seems to be little known, and therefore, of course, is of more value, and no example of the kind has so far appeared in this column. Though the key to it is obscure, it is possible that the reader may hit upon it at once, for he will find the method employed in constructing it is uniform throughout. The passage contains 29 words, and in the original text forms one sentence of good English. TKIQ REXHPJKIXC JSI XNIK JJOKS TKNEQS XYSKAQE KEGJASQSXEKM OKT YNKA LAJECKNOXC REXVOKCQSIJD XEKHQT KOT EOULXC NOXSRKEQP REXBMQUNK DXEZIKROXHTQUAKNQU XTAK HOT XNAK QHXTIKW XRKOQF YRKXANQIDKRXOJ XELBKISQSJOPKMXIJ XECKNEJDQURKP KTSOJMKLAX XTIK KEQB KDLQUOXW.

SOLUTIONS OF LAST WEEK'S PROBLEMS. LOST THEIR ROAD. The distance from starting point X direct to Y is 50 miles. TWO ARMCHAIR POSERS. (1) Two hundred and twenty yards, the size of the inner plot being immaterial. (2) One hundred and twenty-two degrees Fahrenheit, and 40 degrees Reamur. TWO CIRCULAR HOOPS. t The larger of the two hoops has a diameter of 25 inches and the smaller one 20i inches. TWO GARDEN PATHS. The paths were 10 feet wide.' The formula is, deduct half the length of the rectangular-plot-diagonal (25) from onefourth the perimeter (35). "A POSER." The 32 letters if placed in the following positions will show the maximum number that may be placed under the conditions: — APO S E R SEA R P O RO S A PS O E OAE P R S ERS 0 A P

ANSWERS TO CORRESPONDENTS. "N. W."—Thanks for item.

" Beta."—Much obliged for the " Athletes " problem, which will appear in due course. "R. M." —None on hand, but available at any bookseller's shop. "Nautical." —(1) Any day of the week, and always the one that occurs when the vessel is nearest to the 180 degree meridian, the extra day being added when travelling eastward and taken off going westward. (2) The calendars are obviously the same in London as in New Zealand.