"NUTS!"

Evening Post, Volume CXIII, Issue 26, 1 February 1932, Page 14

"NUTS!"

| INTELLECT SHARPENERS I = AH rights reserved. 1

| ■'■ (By T. L. Briton.) §

[iJiimnnmiiiiiimiiiiimiiiiuitiiiiiiiiiiiiiuN,,,,,,,,,,,,^} Readers with a little ingenuity "KiM find in this column an abundant 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 a sledge-hammer to crack them.

A PATIENCE PUZZLE. Here is a little problem which may require the exercise of some patience before -the correct method of solution is ■discovered. The puzzle can bo demonstrated on an ordinary draught-board, a counter forming the only other equipment necessary, and although the problem is of ancient origin, it is still one of the "stock" solitaire games. The counter is to be placed upon any chosen square, and moved horizontally or perpendicularly an the board so that a "visit" is.made to every one of the. sixty-four cells once and once only, the successful demonstrator being the one who can accomplish this in the fewest number of "moves." A "visit," means 'any cell.or cells passed over or made a stopping place, and a "move." in either of. the. 'directions; mentioned cannot exceed eight cells, ■which is the full length of. the' board. ' It is obvious that by visiting squares more than once the number of moves <;an. be reduced, but as already stated it is not permissible to ■visit a. square more. than.once, excepting that the "tour" must begin and end at the same. cell. There is an alternative route from ~any: given square, anH. if the sixty-four squares be numbered they-can be more readily identified for this purpose. This puzzle should interest the many readers who have from time. to. time asked for an occasional moving-counter problem. PRIZE MONEY. The captain and crew of a small steamer which towed" a vessel into port, a distance of eleven hundred miles, numbered forty, all told, three of whom were officers in addition to the master. The: tribunal dealing with' the matter awarded the-sum of one thousand pounds to be divided between them, the captain(to receive four times as much as an officer, who in turn receive .'six' shillings .for every . one shilling md sixpence given to each member of the crew. The basis.oftho allocation was the respective salaries',and wages of the whole ship's company, and the question is if the Amount' of. the award to be received by the. master .of the steamer; was equal to six months' salary, and each of the crew is to "receive a- sum equivalent to a month's ; pay,can the reader find what jhe annual salary of cadi, of the officers is, assuming for problem purposes that every member of the crew received the same monthly pay, and that.the three officers were; receiving similar salaries? .This, is, .merely a simple1 arithmetical question as an antidote to the previous problem; -which, required no-mathemati-cal, skill. •■ ' ■ • A TETHERED ANIMAL. , A correspondent has written to request publication of a "tether" problem of which he gives only skeleton data, but sufficient to realise that a solution is not possible except by the use of trigonometry, and therefore quite unsuitable for the average reader. Most of these "tethered animal" questions are of an academic character, "but in order hot to disappoint the sender of the inquiry, here is one of the kind that can .be easily solved by elementary arithmetic. A long straight hedge of an edible plant runs along the south boundary, of a square i-a'cre section which adjoins an unused road where an animal is tethered. The peg iii" the ground to jwhich the tether rope is fixed is exactly five yards in direct line from the hedge,, and the length of the tether permits the 'animal to graze thirteen yards distant from the peg,in any direction, the road being one and a half chains wide. Assuming that the animal can graze only to the length of' his tether, can the leader say what length of hedge'is at his disposal to nibble at? ANOTHER HEDOE. : "Here'is another problem concerning a Kedge, which the' reader may find somewhat less easy than the previous one, and. may require him to don his best cap" when tickling it. The calculation in itself, however, is not by any means difficult, being well within the capacity of a sixth standard pupil, but to find iiow to proceed may give a little trouble at first. A square block of. land, sixty yards, by sixty, is fenced on its four sides, and on its eastern side a, larger section adjoins, which is in the form of an oblong whose western boundary forms the eastern line of the firstnamed block, both sections having a frontage on the south to a road running duo east and west. From a point "5" at the south-eastern corner of the larger section, a hedge runs in a direet'liiie to the north-western corner of the square block, cutting through the eastern boundary of that area at a.point "Y." There is. a gate at the southern extremity of that line of fencing which opens on to the-road before mentioned, and the question is how far is tho-gate from the point "V," where the hedge cuts through the.fence? '~.-.'' EXCEED TWICE 444. 4 As the reader knows, it is possible to so place the digits one. to nine in a "nine, square," one in each cell, that the number represented by the digits in the; top line 33 half that in the second row, and onethird that in the third or bottom row. In fact, there arc several such arrangements of the. digits in this form that will produce' the same results, but there is only one set of positions for the figures to be placed in which the three digits at the bottom, row of the square represent a number exceeding twice 444. Can the reader find what this number is, and incidentally tlie numbers in the other, two rows, which of course follow automatically? One condition only is imposed, namely, that the number in the bottom row must contain a digit not exceeding 5. There f is no formula that ivill enable the correct arrangement of the digits to be quickly determined, and The search for it. should be more enjoyable for that .reason, especially if the reader adopt a system of methodical trials. ', .'..'.'

first or-last day 'of :'ev'efy' alternate ■'•• century "must be a "Monday. '■' "Mercury."- —lt- can be argued that the part, of a magnitude may be equal, to the whole of it. Thanks for comments. "Another Teacher."— Perhaps "unorthodox" would bvmorc correct than "inconsistent," Nr the problem is capable of solution as shown in this column, and the .. ... professor in-stating it in that way gavo .the. candidates a chance to ■ show that they Are not slaves to stereotyped forms of expression. Two other readers, D.M. and H.M., also-wrote-interestedly on the matter. '

Correspondence, should be addressed care' of P.O. Box 1023.