"NUTS!"

Evening Post, Volume CXI, Issue 74, 28 March 1931, Page 25

"NUTS!"

INTELLECT SHARPENERS ' All rights reserved.

(By T. L. Briton.)

Readers with a littio ingenuity ■will find in this column an abundant store of entertainment, ana amusement, and the solving or tho problems should provide excellent mental .exhilaration. While some ,' of the "nuts" may appear harder than others, It will bo found that none will require a sledge-hammer to crack them.

CW A DIMINISHED DRAUGHTBOARD. .

Here is a '^square" problem a little, different from, but somewhat reminiscent of, "Tho Walnut" puzzle published I with an explanation of tho method' some considerable time ago, in which the solver was allowed to make use of squares outside the diminished board. Take a squaro of twenty-five on a draught-board or a diagram would do equally as well, and number them from left to right one to twenty-iivo beginning at tho top left hand corner. Then take nine counters lettered "A" to "I" and' place thorn on the central nine squares in alphabetical order, counter "E" occupying squaro 13. The problem is to remove all counters from the board (in tho ordinary way of playing draughts), except counter "E," which, if moved in the progress of the play, must be in its original position at the end of the game. Moves may be mado in the ordinary way of "taking" a piece and also may bo made horizontally or in a perpendicular direction, and any counters passed over must be removed frv.ni tho board. For example, "D" could tako "G" and rest on square 22, then "E" could take "H" and "D," resting on square 21, and so on. One move could include any number of counters taken in sequence. What is the'fewest number «£ moves necessary? AN OLD PALLACY. A correspondent'has written to , ask whether it is possible by mathematical process to prove that two things of the same fixed value or quantity are only equal to one of them, and states that a decision is required to settle a wager, his friend assorting that he has mathematical proof. Well, on the lace of it the assertion is absurd, though "had the evidence been required in any other way, some kind of "proof" may perhaps be possible. But not in mathematics, which is tho only exact science wo have. But there is an old fallacy which has perplexed many people who have not bothered much about the study of figures, and for the information of thoso who, have not seen' it, as well as for the amusement of those who are aware of the algebraical process which leads to such an obvious impossibility^ the "alleged" proof is now given. , Suppose that A uquals B, thon A squaro equals AB. Therefore. £. squaro minus B square equals AB minus B squaro. Divide each side of the equation by A minus 3 and the result is A plus B equals B. Then by substitution 2 equals 1. As tho inquirer has asked for an opinion to settle hia wager, I decide that it bo 1 **drawn," because before a person can lose, he must first' have a chance of ■winning, which tho correspondent's friend obviously fcadLaot. REVISITING HIS SCHOOL. A former pupil of one of the city colleges revisited his "Alma Mater" "recently, and amongst the interesting photographs which ho brought away with him was one of a group of thirty-two, including masters and boys who all came from the visitor's homo town. Let us suppose for the purposes ,of a little problem that the photograph showed the visitor in the centre,of a single row, with sixteen on each side. Commencing from one end each succeeding person up to and including tho former pupil was one year older than the ' one preceding, and continuing on each person, including the visitor, right down to tho boy at the other end was one 'and a half years less in age than the person preceding him, tho youngest of the thirty-three in> tho group thus "being at one end, and the youngest in hi» half of tho group ibeing at the other end of the line. Now, if the total ages of tho whole of tho masters and boys in. the photograph wero 650 (six, five, nought), can the reader say how old was tho visitor at the time?

' AN UNNECESSARY WALK. Exactly one mile and a half north of a point B op. a, main highway, two perfectly straight roads branch off, the main road continuing' due north While the two branch routes run in a northwesterly direction approximately, the ' more northerly of., the two ■ running direct to a mailbox and wayside inn ■at M, while tho other track ran direct to a.point- P thence direct • to-M, both 'these roads leaving the main highway at X. A man left Bto walk to X, thence direct from-that point .to" M, but from the turn-off he travelled direct to P before ho found his mistake. Tho road went no farther in that direction, but turned more northerly to M, and upon finding that the road from X to IM, the one he should have taken, was exactly three miles as the crow flies from P, he walked direct from tho . latter place to his destination, tho distance of that "lap" being one and a half miles less than tho mileage he had already tramped to P. By tho aid of ;„ diagram only and without using pen •or pencil to make a calculation, can '. the reader say how many unnecessary , miles tho man walked? \ TWO DECADES AGO. \ Auother one for the recider who pio- ' fers a mental stimulant that does not ] require him to leave the Armchair to v ' arrive at the correct solution,,of• the question involved. When Adam married hi* present wife two decades ago, ho wag. half as old again as she, their united ages then being seven years more than the wife's age now, while Iheir combined ages at present are five years less than double what thoy wore then. If the difference in their ages is represented by half the number of years that madame was old on their wedding day, can the reader find without the aid of ■pen andponcil, what the respective age 3of tho couple were on that auspicious day? These are the kind of questions that provide more fun when ,the would-oe solver adopts a methodical system of trials than by finding the result by orthodox arithmetical process, and for that reason other details aie omitted. XAST WEEK'S SOLUTIONS. A Cryptogram.—More and more tho name of Wordsworth stands.out as that of the greatest of those great men to whom we owe the miraculous new birth of English poetry ono hundred years or more ago. lie had his weak moments no doubt, but it is the great momcntß of a poet that matter, and when we remember Wordsworth's wo agree with Mr. Lascelles ' Abercrombie that in virtue of them he stands third among English poets. Two for the Armchair.—Jim had 2a Id, the total for the seven boys being lls Id. ( ' Fixing the Guilt.—As tho chauffeur, was 180 miles from tho scene at 7 a.m. and the butler 140 miles at 8 a.m., neithe* could have been on the scene Tutor than one o'clock, half an hour bofow 'the crime waft committed. The

gardener could not liavo Joft earlier than 2 a.m., so lie must liavo fired the shot. ' , A,' Mental "Breather."—£4ooo, £2000, and £1500. From Cover to Cover. —Two and three-quarter inches. ANSWERS TO .CORRESPONDENTS. "Curious." —The methods of determining the arrangements referred to are lengthy, and' iv most cases they are not easy. J.C.L.—The. fallacy lies in the use of the word "never." "Inquirer!."—Tho couplet is:— "Large'fleas havo little fleas upon their backs to bite 'em, '> ■ And little fleas have lesser fleas, and so ad infinitum." ' (',,.„ "Student."—Zeno's parados "Achilles and tho Tortoise" was, to confirm his view that the popular idea of motion i's self-contradictory. "Korea."—A "chon'f is a currency of, Korea, and is equal to tho Japancao "sen"; (2) Governed by Japan.' Correspondence should .be addressed to P. O. Box 1023.