INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20514, 15 March 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

A TRIANGULAR " DUEL,.' 4

BY T, r.. BRITON.

This " duel" was in the form of a cOm« petitive series of games between,three persons, who may be called A, B and C, As in most games, there was something tangible depending upon the results, and' in this case they were shillings; but oio winner of a game did not receive from the others, the loser paying out to the other two, and each played for himself without any combinations or partnerships. They all startled with a different number of shillings, which were placed on the table :iu front of the respective players, and tha stakes were level. " Aaron" lost the first game, and, after paying out,' Benjamin and Cohen found that their money was thereby doubled. Benjamin lost the second game, and Cohen the third, each of these games doubling tho money of the Winning two players. If, after tho third game, Aaron had twice as much as Benjamin, and tho latter twice as much as Cohen, how much did tha players win or lose if at the finish, the latter had six shillings less than Aaron? Pen or pencil should bo unnecessary for this calculation.

, i A 600-GALLON TANK. i y An empty cylindrical water tank'having a capacity of exactly 600 gallons has a pipe attached to it leading from a reservoir, and when the tap is turned on full, the tank will be filled in 120 njinutes. There aye also three discharge pipps connected to the tank, which may be called A, B and C, and these, working separately, can empty tho full quantity of 600 gallorfs in 12 hours; 10 hours arid six hours respectively. There were already 75 gallons of water in tho tank on one occasion when the inlet pipe was fully opened, and exactly half-an-hour afterward the three pipes, A, B and G, were opened together to their fullest extent, the four pipes being shut off simultaneously, three hours and 50 minutes after the supply pipe was first opened. As the water had not reached the top, how many gallons were then in the tank ?

PILLED AUTOMATICALLY. The previous problem suggests another in tho same vein, but somewhat different in detail. A small water cistern has three jets, or taps, which automatically fill the vessel. The water does not flow continuously from them, but at different and regular intervals they discharge cer r tain quantities into the cistern, the time ./ occupied in the actual discharges being negligible. Let us suppose that the smallest jet, A, discharges instantaneously into the vessel one pint of water regularly at the end of every three minutes, that the second jet, B, discharges in the same manner one quart at the end of every five minutes,, and that the largest jet, C, lets into, the cistern, by a similar automatic arrangement, one gallon of water at the end of every seven minutes. Now, if the capacity of the receptacle be 53 gallon:;, at what timo would it be full if the first three discharges'into'it from the jets were one pint at the end of three minutes, one quart at the end of five minutes, and one gallon at the end of seven minutes,' starting from mid-day, maintaining these rates throughout until full, and what quantities would the jets have discharged respectively? I

WHAT IS THE TRANSLATION? Some time ago a letter, written in a strange code, which had' been brought under notice by a correspondent, was published in this column, to give the reader an opportunity of exercising his ingenuity in finding what it was all about, and, judging from tho correspondence received at the time, few succeeded in translating the curious epistle. Here is which, though apparently not in the same > code, has" much in common with tho firstmentioned letter: - . Egan not labol gtsni aga sase iro getacyb metsy sagciru ova fac irem afos etits do tinu eht dna nia tirb ta erg; det po - daeb dlu ohss noit atimil fono itac ifis . sale tah wots as eirt nuoct neref fideh tfos lasop orp eh tsa wad nega eh tnome tifeih" ceh tec neref nocla va neht fono isse syra nelp drill tehtta. Can the reader make anything of this, for it does not require a knowledge „of any foreign language 1 0 sir-, 1 COLLEGE BURSARIES.

The 12 winners of bursaries last year, as well as the 18 " consolation" winners, came from' three colleges, X, Y and Z, there being a total of 180 candidates competing for these prizes, the total value of which was £l2O. This sum, however, included the 18 subsidiary rewards called " consolation prizes," so that altogether there were 30 winners out of 180 contestants, and the figures are adaptable to a simple yet useful little problem, suitable for theso 180 young students after their more strenuous " bursary" efforts, as well as for other readers of this column. Among the 20 prize-winners the average amount gained per student in "X" college was equal in value to two-fifths as much as the whole that those in "Z" secured, and to two-ninths of the total value gained by the successful "Y" students; all the latter gained one and four-fifth times the value secured by "Z" candidates. There were three times as many "Y" college winners as 11 X" had, and half as many again as in " Z," so, assuming that the successful ones in 11 Z" totalled twice those in "X," what was the value gained • per student in the three colleges, and how many were successful in X, Y and Z : respectively, LAST WEEK'S SOLUTIONS. Baying A Section. The shopkeeper bough the whole quar- • ter-acre section, with 75ft. frontage, "at £l6 per foot, and sold 60ft. of it at £lB per foot, thus securing his 15ft.. at £8 per foot. . : Fair and Head Winds. The time would be longer with the wind influence, though possibly there are some who think the times occupied would be equal, Christmas In An Orphanage. There were 253 bags at the commencement, so the numbers distributed on each of the four occasions were 63, 47, 35 and 26; total, 171. Four were given to the caretaker's boy, and 78 were not distributed. Two For The Price of One. The answer is £lB7 10s, each showing a profit of £37 10s, when sold singly for £225, the same as that on three sold; to one buyer for £6OO . Score and One Fair Maids. The eldest was 26, the youngest six, the eighth youngest 18. ANSWERS TO CORRESPONDENTS. CTM.—'The smallest number is 144, the 'next 516, but there are exactly 18 numbers in between these tuo j all conditions, except the one mentioned. Curious.—You have tasen something for granted, and it has " let you down. Though it might succeed in some instances, the practice is unsafe ; and not mathematics. . - Statistics.—There are more jpeople to a the square mile in New Zealand than m Australia or Canada,- the- approximate numbers being 14, 2.1 anil* 3.6 respectively. Great Britain has " about 500"; to every square mile,'and nearly; 70Q m Eng-* V land, ,