"NUTS!"

Evening Post, Volume CVII, Issue 10, 12 January 1929, Page 27

"NUTS!"

INTELLECT SHARPENERS i '.- All rights reserved. j

(By T. L. Briton.)

1im..m.«.»-..,n. 1 n. „,,,,,,i,u«,,A \ Readers 'with'a. little ingenuity will find In this column an abundant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilar&tioni. Bom« ■ , of the ' 'nuts' 'mayappear harder , than others, it -will 1» lorind that. nons will require a, aledge-hiinmer | to crack them. •'.••■••" ';■: ::t "■""•..'■ UNCLE AND NEPHEW.:: A.gentleman who was givpn to spoaking enigmatically was; remarking t to some friends upon the' excellence of an Operatic performance ?ie had witnessed the -previous evening, when in the coui-se-of conversation he said that his uncle and nephew accompanied him to the theatre and that he had purchased the necessary admission tickets for the party.^-It appears' from the information supplied.:to hii ■heaiers that he tendered a &5 note at the box-office and received the required tickets, together with £3 10s change. Now, here' tcomes the en-, igma. The gentleman stated further' that the change mentioned was right,, though the tickets cost'lsa each, adding that the ■ number'and value of ..the tickets were alsd; correct, and.this.'the; ticket clerk conflrmedi Can the reader" say how this could be possible,' in view, of the fact;.thai none of.the party-were;' on the free list, full prices being paid; for each.' '■.'■'■'•.'/^•.'','.•.". ,'.. -j^v- I.' ' ':-'{--: THREE .TIMEPIECES. In a certain- Government Department there wer'evthrce clocks, none of which could be relied upon ;for:- the correct time. One gained uniformly',lo minutes per week, another gained 15 minutes, in the'same time, whilst the third lost regularly at the rate of 5 minutes per week; ''That was their record when tested) and the expert who was called in .to. regulate and adjusts them first. allowed 'the three clocks to run on, each at its own uniform rate mentioned until: the three' timepieces showed the same time. : Here is a useful little problem' 1, suggested,"by these facts. Supposing tha|*;at noon- to-day, Saturday, 12th.January, the hands of the clocks' showed, 12=: o'clock together, and were allowed,itp:'ruii on at the respective, rates" described, can thei reader, say when the three timepieces will) first show identical time again? To obviate any-possible confusion in writing a.m. and 'p.m., <the .reader may adopt the practice now in vogue .of ■writing tha hours as from 1 to 24 o'clock; for. example, 1 p.nij would be in this way 13 o'clock. ;: ; :'! ■;., -'■ • ■■?. WHAT TIME WAS IT? A very simple every-day question is' prompted;by the, previous .problem. Before? Btating.it,.however,.the,reader will quite that in calculating problems concerning measures of time it'does not necessarily follow that the correct solutions can always be indicated on the dial, for some results may ; involve fractions of seconds which no .ordinary chronometer can show. The following problem, however, will a-oquire a solution only to the nearest half-minute, ignoring odd seconds and fractions. Upon looking at my wate'ii b.-.!\Vi^Vn"; 4 and 5 o'clock to-day,;and again ibetween 8 and 9 o'clock, it was noted that the hands, had exactly changed places. ;Now'.by examining a dial it would'be "easy lb to a minute or-so the exact-times/that I .looked at the j'wateh,,l>ut ..can. the, reader make'the' inecessary calculations i- and "find to a

half-minute wiiat those times were? The. arithmetical process is quite a simple one. -: MADEIRA WINE. . A wine taster blended a "Madeira" from four grades of wino under instructions that the mixture should bo worth 17s 6d per gallon, ISased upon the quantity and value of; the four wines comprising it, which'jiiay'be designated "A,"""B,"."Cy and "D." The values were all different, the highest being A grade, the prices descending to the inferior class "D." The tastermixed one gallon of "A" with .three gallons of "D," and one gallon of "C" grade with-two gallons of "B," putting the whole into one keg. In this way the blended'wine was worth 17s 6d per gallon, based on the individual prices; "A", and "B" being-each priced more tlian this sum per gallon; whilst "C" and:"D". were each of lower value than ;17s 6d. . \From these details can the reader crack this little "nut" and find what : was the price of each grade? . IN ALPHABETICAL OBDEE. Ingenuity rather than theoretical knowledge will be required to solve the following little puzzle:—Arrange the first twenty-four letters of the alphabet in the following order of four rows with sis letters in each, and then find out the fewest number of exchanges required to place them in alphabetical order. This little problem will require much, thought before it .can be solved in fewer than "eighteen moves, for, althbugh two letters are already in their proper"places, and the first three moves, ,"A," <<B ) " and "G" are obvious, a little difficulty.will no. doubt be experienced before, achieving.' the correct result. An :'fexchange'" is merely transferring one .letter., and', putting another in its place,' ■and ■there is no limit to the number ,6f 'times ..any letter .may be, moved. -, ~-,:^'W'M- B. "O.: H. 'U. ':<^.:-.q; m. k: x. l. j. "■■■■.'. :M. I. P.: d: T.'-'K. .•■■•■. -;; c ,:'s::.'g;-'AV". -n;; v.-' k. ... "■■".•" .If any-reader should succeed in accomplishing thisi in seventeen moves, it will,(in the writer's opinion) be tho fewest possible, though it is claimed to; have been done in: sixteen exchanges. -."! ' LAST WEEK'S SOLUTIONS. A; Mathematical Letter Sorter.-^-ThG number of the house to which the letter, was addressed, was. 35, there being 49 ■ hduses : ; oriithat side of. the street. A IPossible Error.—The number to be multiplied by:, 106; is -223 the: product being 23532. Byiplacing the figures in the wrong'positions as; described but otherwise rcorreetly multiplying, the product would be 3552, or 19980 less than the correct resulK : . . . Coincidences at. Cricket.— "V" team scored 128 and 72, and.f X" 96 and 54 runs,, the former thus winning by 50. run's.' " '.-' >. ■...:■•■:': ■,-'. •;,■ ■ ■ V' ; Twro Armchair Questions.—(l) Half a pint.of water 'was'.,added' to each quart; V(2); under the v;/conditious 150 apples -could ..be' purchased ' for .the sum named. ':•■:'■!■"•■';'.■'', ;:' " :■. :i . Eureka.i T -r6ne method is .as follows:— 12 to:e,7 : :'to i-,10 to E,.;8 to A, 9to U, and 11 to..k.';' n .,, .\' "•'./■■■■/■ .;'': '"'.■ ■Answers.'(to Correspondents. "ScaooliV.ij-fes, it could-.be treated as a "quadratic," but why "fly so high?' when simple arithmetic supplies the process? ' "Caught Out."—Yes", the average would be as you say. "Avoirdupois."—Add the ten weights and divide by the dift'erenco of the highest and lowest. "Appreciate."—The theoretical result in any case is always determined by the' relationship between one of the .two movable objects and the other. It is a very useful formula to know.