"NUTS !"

Evening Post, Volume CXIII, Issue 15, 19 January 1932, Page 14

"NUTS !"

I '■'/>' " ■: ■ ..■''': 1 I "(ByT. L. Briton.) I il, ■_.'■ ■ X

j INTELLECT SHARPENERS 1 | All rights, reserved.- f

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 exhilaration. While Borne .. of the "nuts" may appear harder than others, it will be found that none will require a sledge-hammer to crack them, ~■■"- --l FOUND IT." Here isa little poser which should •; interest the reader, and particularly the lover of ;counter-inoving puzzles. Make a diagram of the dial of a timepiece, omitting the hands and also the ■ : hour-numbers 2, 4, 8, and 10; and draw i our lines direct from the centre to the * hours 12, 3, 6,9. .^Then take, eight i counters, and mark each with a. letter contained in the words "I found it," distinguishing the capital and small "i.V Place the capital "I" counter 'on the hour 12, "f." .on the 1, "v'"' \on jthe 3, "t" on the 5, "d'?,oh the 6, > O on the1"?," "n" on the 11, and' the small "i" at the centre. The" puzzle is to arrange the counters un- ' der the following conditions, so- that v the letters form the words.;-'.'l found it" reading from right to left; ,the. : centre being then vacant. The coiin- ? tors should.be move.d one. at a time, ■to or from any position to one adjoin- -.; ing if unoccupied, and-when, moves are :'; being made to or. from; ttie centre the counters must travel along the linea prescribed. They niay^be moved in the same direction, or ; .-to. that taken by tho hands of'a clock, except .of course the moves'to or from the :-; centre, to which that Condition' could not apply. A. counterV-may not be '-; "jumped" over, nor may itwo occupy ';- the same position at the same timei'and . ; one of them must.not be,moved at all. 5 The reader should note the word 'fad? \ joining, '' .and'.ifhe/c'an achieve the de- ', sired result in fewer than 17 moves; ■; a record will have been made. ; UTILISING THE SPACE. The problem concerning a method of economical packing which appeared rS- .: cently has prompted "New Header"''to. ■'; send along the following, which is ; arithmetically very'simple, though at ; first it n>ay not appear so. A quantity of gold bricks were- being packed in boxes of, equal.capacity, and. the size of them,is wj;at;the reader'is asked to' determine from the following information concerning the.jnetal slabs .which,; ; when packed, utilise all the space available, their-uniform size : . being inches and, a half in length, eleven - inches wide, and one' inch thick. The ; question-is,-if it is required to pack -\ these into rectangular boxes of uni- ■ form size, in.'such manner that riot more I than twelve are laid on their edges, what should .be .the inside, measure- . ments oif a bos 'having equal length ■ and breadth, if eight "hundred of the '- size stated vaie packed into it and "< utilise the whole of the space? This .: is quite a useful question, and tp find ■ the .particular method of packing under the ; prescribed conditions should afford the reader the opportunity of esercis- ,• ing his ingenuity, though the arith; i; metio of it is,very simple. .< J STTOYIN& ECONOliiy. ' The late Sam; Lloyd was' probably, the , first of modern '"problem-makers to * formulate a puzzle concerning the re- :. making of: a broken chain, and here -;! is one of. his-improved by. H. E. Duy deney, the well-known London mathematician, which should give the reader a few moments of'hard thinking. A * chain of fifty links in the. form of a necklace is broken into nine ; distinct - parts as; follows: Three, pieces, each containing sis links; another .with three \ links; another with four links; two ;"• with five links; one'piece With seven ; links; and the ninth piece with eight X links; total, fifty links. '. A working jeweller offered to remake these into .- the original.;_form of. the endless chain, > though the links' would not", necessarily ;be joined to. the actual ones as before',1 ;■ and to charge-for the work at the'rate' ". of fburpence to: open a link and eight- > pence to'close it. Before the owner accepted the offer, ho ascertained that a new one of the same size could be :; purchased at the rate of twopence per "' link, namely^ for eight shillings and . fourpence. Assuming that when mended the old chain : would be equal in all : respects to the one purchasable at the ,; price stated, can the reader find which : would be the morejec'onomical transact i tion to the owner? • ■■" '"' '"' ' ' \ FOUR, BROTHERS. . •' . A keen problem-lover, ■ C.J.W., cvi- '•'• dently dbWnot allow his annual fur- •; lough to interfere with his interest in -. this column, for he'has sent the following little problem from his holiday ~ reaort. It is, in one respect, similar i to others received from this correspondent, in that "fincling the way" --, requires the^hard thinking, rather than : "travelling the route." Matthew, like his three brothers,, two of. whom are younger *than he, hag not yet reached v his fortieth birthday, arid the number '. representing' his age in years'to-day is '.j the product of two whole numbers. If those two numbers are each reduced by»two, their,'.product' would represent the age of- Matthew exactly eighteen years ago, and, strange to say, these : details are' also true concerning.! the ':'■ ages of the other three brothers. ..Can, the reader find from these facts the respective ages of the (four people? Possibly many would-be solvers will scorn the use of pen and pencil in finding the ; correct answer, though. the. sender of the problem does not stipulate this. \ FOR THE ARMCHAIR. «,.• 'No ,floubt the reader who sought the "assistance of either pen or pencil in. : solving the previous • problem will ig 7 nore their aid for this one. It is not "■ difficult in; «any; way, ;-and 'G.J.W.' de- ' scribes it correctly when he states that the answer should be obvious after a J couple; of minutes' thought. Every ' afternoon in the; week ,a "gnidie accompanies a party ofcto'uristsVto one ..of the scenic attractions not far from tho hotel .where' they preside.;, 'The; party travel; there arid "back''in a bus driven by the guide, and the fare charged for each person is at the rate-of one penny per mile travelled in the vehicle. Ee;centlythe guide was given a month's holiday, and ' during his'absence 'another man drove - the: bus, and during that period of duty, the substitutedriver, collected fares at the rate mentioned to the- amount of > £17; 3s ,7d (Seventeen pounds three,, shillings and . sevenpence). 'As there was only one ■ trip there and back made daily, and ' every seat was occupied on every occasion, what is the distance from the : hotel to the spot referred to? SOLUTIONS. 'An Poser.— Two men in to the/four already employed would; complete the work in an extra ; day. ' The examiner sprinkled the with a little humour, as the ■ boys contributed nothing.to. the.results. Fitted Exactly.^-^rqm a . point on one'side'three inches from the top corner cut ;four,-inches parallel-to the top, then four inches parallel to the Hong .sides. Eepeat these two cuts, and make a final one of three inches parallel to

the top. The two pieces will bo'found to fit and make a board one foot square. , . '•,-, "_- ,' A Square .with Circles.—lf tho four pennies are placed heads down on the table, they can be so arranged that the four lines above the dates will form a square. • -.-.-- One for the Armchair.-—The fust day of a century cannot fall on "a. Wednesday. .'-.■■■■ , . V: ■-■-■ Payment in Kind.—Seven received thirty cases each, and the eighth forty cases from the total of 2000 cases.