Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21414, 11 February 1933, Page 5 (Supplement)

Intellect Sharpeners

B? T. L. BRITON

AN ARMCHAIR POSER .

Here is a question for the reader vho favours one which requires a minimum amount of calculation. A returned uncle was inquiring the ages of his two nephews, his sister's two sons Jack and Tom, the mother having been at boarding school when the uncle left New Zealand a genet <ition ago. Jack, the elder of the two,- put the answer in the following enigmatical form " I am now twice as old as 'lorn was seven years ago, and after the lapse of another period of that length from -y . now I will be half-as-old-again as Tom is now. Our united ages then will be represented by the age that Tom will be in ten years from now, but with the figures reversed." The simple question is what were the respective ages of the two nephews at the time of the conversation ? As a condition of the poser is that the correct answer should be found without the aid of either pen or pencil, it may ba given in an even number of years, omitting fractions if any. If any suggestion ba needed to help the would-be solver from tripping, it is that the stateirysnt be read carefully and the tenses noted. In reading through the question after writing it, thi impression is formed that I have unduly simplified the problem,' but in what manner will be left for the reader to discover, which in itself may' provide intellectual amusement. " r " : COST or A GIFT Four girls decided to give their teacher a birthday gift, and the tramfares and afternoon teas in town were included in the cost, which the four girls had agreed to share equally. They decided upon a gift slightly more costly than at first intended, and though they had 34s left altogether, which was more than sufficient for their purpose, some of them had not brought enough cash with them. They therefore " pooled" their resources amounting to the sum stated and arranged their individual accounts afterwards. The transaction at the shop was completed by tendering the 34s and receiving the change which was an even vmmber of sixpences divisable by four without remainder. The following particulars indicate the sum that each girl had brought with her to the shop, and from the details given the reader will no doubt readily find the respective amounts which is the point of the question, for, when that has been determined, the cost of the gift will be obvious:—" A's " quota to the pool of 34s was fifty per cent more than one girl's share, "B" could only put in a sum that was 2s short of the proper amount, while " C " had with her only half her quota to add to the " pool." " D " however was able to augment the fund by putting in 4s more than the quarter share of the cost of the gift. How much did the girls spend upon their teacher's present ? THREE TIME QUESTIONS If a person upon being asked the time of day, replied correctly that an hour and ahalf ago it was twice as many minutes after mid-day as it is nowjlminutes to two in the afternoon, what time was it then ? \ If I set my watch right on the first day. of the present month at noon, what time will be indicated by the hands at noon on the twenty-fifth of the month' if the watch uniformly loses two-and twofifth seconds daily since being put right on the first?- *- • " ' What fraction of" their sum' is the differenca of three-quarters of four hours forty minutes and four-thirds of one < hour forty-five minutes? These three questions have been so stated that they may be readily answered correctly from the armchair, without of course the aid of either pen" or pencil. DOUBLING THE STAKES " J.C.L." sends a problem concerning a series of games played between two persons in competition. They played six " rounds" altogether. After the fourth game the record was two wins each, so for the two final games they agreed to double the stales,-making the; points'"six. pence each instead of threepence as wai the case in the first-four games,? As a result of the fifth contest " X " won from " Y " a sum equivalent to 40 points, but in the next game,, the last of the series, the latter won from his rival two-thirds of the money that " X " then had which of course included the pound that he won from " Y " in the fifth round. They both commenced with similar sums of money and played for level stakes, and the question is that if at the end of the' sixth game when a complete settlement was made between the players under the termsstated, Y" had exactly four times more money than his opponent how much did; they start with? The .reader, will note thatHbhis question is purely one-I&be cor-rectly-answered from the armc]i£i& though the \sfcnd6r of the problem : has- not expressly, made it a condition. EVERY FIGURE DELETED Sometime ago a " restoration " problem was published in this'column- from which every figure of the sum (long division), was deleted, and a correspondent " Rex '* has sent one of the same kjnd by Mr. A.C. Corrigan, which the sender discovered i in an old magazine, but not the solution. It is an excellent example which should provide the reader with an opportunity of exercising his reasoning faculties, for the complete sum can be reconstructed by logical deduction. The would-be solver of this interesting puzzle will not fail tq take advantage of what seems to be the kernal of the problem, namely the four places of decimals in the answer, though ' unlike the quotient in the previous pro--1 blem of the kind, it is not a repeating ' decimal. Without this decimal in ' answer of the present puzzle, a solution by ! deductive reasoning would be very difficult to reach. The divisor contains three figures, the dividend six, and the quotient is a whole number of four figures with a ! similar number of the decimal part, sum having no remainder. Further clues 1 that should not make the restoration too obvious are that there are five lines of ' multiplication necessary, two figures must be brought down in the first substraction I line, and that two of the ten -digits and cipher are " conspicuous by their ab- ' sence " from bpth the sum and working. I I hope that the author of this excellent , puzzle will not consider that these clue* give an undue advantage to the solver., Without them the puzzle would be extremely difficult. > LAST WEEK'S SOLUTIONS 5 j Chairman's Casting Vote.-—72 people r present, the first count being 40 and 32. OB the Beaten Track. —The respective " equivalents of " X." and "Y " are eleven ' and four, so that he.was born in 1892 and " died in 1932. . . Pour Candidates.—The number of votes J for the four candidates respectively weu s 2100, 1750, 1400 and 1050 a total of a excluding informal votes. - r Poser to Tto.ac.-Th. W»^ ere " : ' * i i.P-rt. b.ing £7SO ~« " Sam.—The.onjy