INTELLECT SHARPENERS

Otago Daily Times, Issue 20354, 10 March 1928, Page 19

INTELLECT SHARPENERS

By T. L. Briton’. Readers aro requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on tho Saturday following the publication of the problems. MONETARY EXCHANGE. When moneys ai’o required to be remitted from one country to another, it not infrequently happens that circuitous instead of direct routes aro adopted in order to take advantage of any favourable rat© of exchange that may he offering at the time in any particular place. A seasonable problem on the subject is offered tor the reader’s consideration, in view of the increasing trade that is developing between New Zealand and South American States. A firm in Buenos Aires desiring to remit £762 to a New Zealand bank finds that the rates of exchange are as follows: —Fifteen shillings equal 27 pcsestua in Buenos Aires ; £1 sterling equals 4dnl 72c in New York, where 3dol 54c can be bought for 27 pesestns. In such a case would it be more advantageous for the firm to remit direct to New Zealand from. Buenos Aires or circuitously by purchasing a draft for £762 in New York? CLOCK PROBLEMS. The solution of a clock problem published recently, gave the time five and five-elevenths minutes past 4, and a correspondent, being puzzled to know how the “ elevenths ” comes in, asks that the method of arriving at the result he explained. “ I can understand,” she writes, “ odd seconds being expressed in fractions of 60, but ‘ the elevenths ’ is altogether a puzzle to me.” It is interesting to receive this communication, for the explanation is one that can readily be followed by anyone, no technical knowledge being required. If we divide the dial of a timepiece into 60 equal parts, it will be noted that the minute hand travels once round while the hour hand moves five divisions, or one-twelfth of that distance. Thus the minute hand gains on the other 55 divisions in one hour, which is equivalent to 11 divisions in 12 minutes. The solution referred to was onc-clevcnth of an hour past 4 o’clock, namely, five and five-elevenths minutes. A GREASY POLE. During a recent festival in a country town, athletic sports formed an important feature, and one of the events, viz., climbing a well-greased pole, gave the public a largo measure of fun. Although no competitor managed to achieve the feat, it was accomplished afterwards by a Maori hoy. Here is a problem on the latter incident. There was a platform on the pole Ift from the ground, from which all competitors started. Another platform was affixed to the polo a certain distance higher up and just Ift from the top. The pole had to he climbed from the lower.platfonn on which each competitor sat, the feat being achieved by gaining a sitting position on the top stage. Assuming that the Maori boy ascended 2ft and dropped Ift in alternate seconds between the two platforms, and that it took him 9sec to accomplish that distance, what was the length of the pole? AVERAGES. Probably no form of calculation is simpler than that relating to averages, yet it provides more pitfalls for the nontechnical person than perhaps any other. One every-day example of this in in tho often-heard statement that it is possible for a bowler in a cricket match to obtain a better average than another in each of two innings, yet be beaten in the record for the whole match. Again, the fallacy that a car travelling out at 20 miles an hour and back at 30 miles per hour, makes an average tor both journeys of 25 miles per hour is acceptable to some persons instead of tho correct solution of 24 miles per hour. Most readers, however, know that given the average of two or more sets of quantities, the average of the whole is not obtained by finding the average of the averages unless there be the same number of quantities in every set. For instance, a boy spends daily during May two shillings and threepence, during .Tune four shilling and a halfpenny, and two shillings daily in July. What is his average daily expenditure for the three months? THE BRIDGE TOURNAMENT. Last month a problem was published concerning the arrangement of parties and opponents in a bridge tournament under certain fixed conditions, and so many readers having asked for the publication of the positions in detail they are given below. The letters ABC 1) E E will denote Indies and G II I J K L the gentlemen. AIL r. ID. EJ. v. GK. F.H. v. C.D. AG. v. JB. FK. v. lIL. GI. v. DE. AD. v. KG. GL. v. 18. HJ. v. EF. AE. v. LD. HE. v. JC. IK. v. FG. AF. v. BE. IC. v. KD. JD. v. GH. AG v. OF. JD. v. BE. KB. v. HI. AH. v. DC. KE. v. BF. LG. v. LT. AT v. EH. LF. iu CG. BD v. JK. Y.T v. FI. BC. v. DH. CE. v. KL. AK. v. GJ. CH. v. El. DP. v. LB. AL. v. HK. DI. v. FJ. EG. v. BC. This may bo deemed useful enough to be kept by for reference. SOLUTIONS OF LAST WEEK’S PROBLEMS. THE GENERAL ELECTION. There are 91,881 different ways that 80 members of Parliament can be formed into four separate and distinct parties 80-0-0-0 being one way and 20-20-20-20 another. A WHEEL CURIOSITY. Th e explanation, shortly, is that the hub of a wheel, though only making the some number of revolutions as the other circumference, progresses or moves along also by the carriage of the wheel. The rim, of course, travels the actual length of itself in one revolution. TYING UP PARCELS. The cord passes twice along the length of the package, four times along the breadth, and six times along its depth. The size of the largest parcel under the conditions is, therefore, in feet, 2 by 1 by 2-3rds. IN A MILITARY HOSPITAL. The number of patients in the hospital must have been 120, according to the records given. A CARILLON. The peal of bells should be arranged as follows 12 3 2 13 2 5 1 3 2 1 3 12 13 2 ANSWERS TO CORRESPONDENTS. A. F. B.—Any surveyor or civil engineer would be qualified for that work. E. S. —Yes, the result agrees with your theoryq and lias appeared in this column already. Thanks. J. B. (St. CHir). —Very interesting, and perhaps wiil r/ake use of when propounding a problem on th’ subject later on. This refers only to 'Tie air-compression suggestion, and not to the “ cardinal points ” matter.