"NUTS!" INTELLECT SHARPENERS

Evening Post, Volume CVIII, Issue 138, 7 December 1929, Page 31

"NUTS!" INTELLECT SHARPENERS

All rights reserved. (By T.-L. Briton.) ""' Readers wittl^ a little ingenuity will find in this,column an'-'abun-dant store of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, it will be found that none ■will require »• sieSge-hamirier to crack them. '&■

NOT UNANIMOUS.

'A number of suburban residents jorm-. ea themselves iifto'a. kind "of "WeJfar? League" to furtKer.^h^'interests of suburb, both socially' ;&nd "■politically, and with such^>^3^4genda c ,it >,was •nly in tho n&ttite/.-ii things that' Tall" proposals subinitie^' at the meetings were not un?i,iiimo«s}y accepted. Let us ■take a receprt'/inei^ent and make it the basis of ■^■'■l.We; mathematical:-prob-lem, for i^teaa.'foi proble-ms^'lhappen"' and are^p^frcieated." This-particur lar meeffiagr.B'rMe up informally, wjion a certaS|>j!i|p.p,g:sal was defeated, anti^ Mumbesfl£.py<jjgi:i6 left the -hallrli Jdlws: had al^p^gopg/ when Ins-niolKeMn-law" took and ' others away, ek-actly-^qae^.fi^lf of the entire meeting ivould/i'ha^&y/with drawn If, however, madanie.HaS been loy.al to her-spouse' and, ri'maii^ed, only 'five-elevenths of tho .total -attendance would have left' the hallj.and only four-elevenths ■would haye,-.\yitharawn it the wifie:' had t^--mained^aia had perstfadedvhet .mptber^ her.'-mpirhei; 's step-daughter,' and- "thi latferTa two cousins to stay-an,d«:.see th^r -thjiig";l out.'' Now in- " tHe read<eir ;toii say how,many werec preseafc before;;th© -withdra-wdl 'it will perhaps fee", nfenec^ssary to suggest.that pen and pencil/sttould be esehewed^ if or,.- the' questions-is clearly one if pi;., the-: armchair. ■}';; " .»■-..'.'' ° '■' ij-.--;. ,;;. IN IHE ARMCHAIR / the reader*has satisfactorily disppsediii the "suburban-:? ' question, here ik v otiß>! that ' hfe' -iwjU; sply,^' -jjuifev.Jßis easily;i.iunder similar" cirtmnstknges; -A property owner at;.nis;M«ath- left one hTttßdrfed and five acres, of land:%/be sabaiyided into ;three"s"eetioris, the areas to be in the proportion of pne-^hifdj' one^fourth, and one-fifth to be.'given tfeach of his three sons A, B, and 0 respectively. The youngest son, C, hpwever, died before the subdivision T^s made and the question is,' how should the block be equitably divided between A and B in conformity with the terms of tjje bequest? Though: a:simple questioni.;it is quite possible" to' catch the unwary: reader.-who does not note carefully"-t%/-t|rms of the" be iqnest and the question-submitted.,,' p/vJHB-'lffliiE OF DEPARTURES A; 'slow train1 travelling on a -non-stop run between P-^-. au a Q_^- ; a distance of one hundred and forty-eight Rules, started from P at 6 o'clock iR. -the.. .morning^ a n d maintained, an Bj&ir fate'TD"*"travelling "■ thtpiighout eighteen and a_ half; nnles.per hour. A "goods" train following "from P-' ajui, IrasreUjng,. to. q^—^- without, stopping, also kept an even speed throughout, though somewhat faster than the strain ahead, the relative speeds being -as--eight- is -to -fiverT-Now -if the - faster train of the two arrived at Q exactly fifteen minutes after the first one, at -what time did the goods train leave the station at P ? HjJNGRY CHINESE SOLDIERS. Tie recent reports from Manchuria that" Chinese soldiers were fighting amongst themselves near Mukden have since been augmented, further details stating that starvation was the cause, and;that five regiments were involved. Letius call them A, B, 0, D, and B, and assume for the purposes of a problem thai!- regiment A had managed to muster two-thirds of a large flock of wild Mountain sheep, and that whilst driving.ithem to an obscure place of safety the^other four brigades espied them, ■whiqh started the conflict over A's lot, the ..balance of tho flock having escaped iand were not in dispute. B first took three-eights and G three-tenths from A, when D came into the " scrap, '' which resulted in taking from A all but'ione-seventh of his original Ititjand' these were secured by E after a :sha,rp fight leaving A- sheepless. D and,',E then each- took one-quarter from 'Bj' when A came upon the scene again and" succeeded in driving off one one-quarter of :C's lot, B also securing one-third, D two-sevenths while E secured-'half of yhat C had left. Three-quarters of A's;j and B's sheep then got on .''no. man's land," but they recovered fiveeig^ths of them, the other three, regi--! meiiits each securing one-eighth. 'Tliis endjed the fighting and the one-thitd of" the flock that got away were thei driven in and divided equally between the five brigades. Now if the total number of sheep is the smallest on&i possible under these conditions, how| many did each company have after hostilities ceased? |AN AGISTMENX PADDOCK. & farmer had a heavily grassed padflock of ten acres which he let for eight days to a drover for the sum; of ■ ten:[pounds eight shillings. The'droverV horses were all similar to the farmer's sto6k, all being draugi't, and-las-the: lessee did not wish to., leave any grass in the paddock at the.^Bffiiofltlie eighth daj^ he regulated accordingly the number;; of horses put inidihe/.33asis;ei\:iiis: estimate being supplied by the fanner, viz.s that seventeen horses;.would >com-s pletely eat off the growing "grass in"'a mo^th of thirty days,;;>nd -.--that nine^ teeit horses would aehievo'tEe same're'-* suit in four-fifths of/:that time. jNow here is the questiofl: - AssSfm'ing''-'thai; the; grass grew uniformly, and that four of (fche drover's horses- v^erel-taken-'out-at £he end of the sixth day, how many howes should the drover 'piit ln-'tihe padi dock, so that the grass would be eaten t>2;in exactly eight days? JiIiAST WEEK'S SOLUTIONS. " - '=fThe Eagle" and "The Hawk."-T-53 miles from V to 2. """ A Question of Profit.—The shop-, keeper made £2 on cost price by sellingi the instrument for £12, as thirty three and a third per cent, above cost, c.nd reduced by ten per cent, represents a profit of twenty per c&nt. on cost, not twenty-three and a third as it .iinight appear. ially Ho!— The "fox" completed th^; course eight minutes ahead of the fleetest "hound." Railway TravelUng.-^A passenger is allowed 1681b of luggage under the conditions set out. A Sale of Gramophones.—3 "cabinets," 8 "box," and-109 'portables." The problem stated that there were more than one of each class, thus limiting it to one solution. The price of each kind was stated in the problem. ANSWERS TO CORRESPONDENTS. F.M.W. —It is not a matter of guesswork, but is to be done by a process <>f mathematical elimination, "framework" —There are only ten different ,JV a-3S. °n. what you state. F.3DiamondcT-Tljio..eorr:eei:.answer is as • already given, viz., 12G0, your mistake being the result of transferring •Ihew-smuigjiumbexs. under "C'j and "P." The other item is O.K.