INTELLECT SHARPENERS All rights reserved.

Evening Post, Volume CXV, Issue 105, 6 May 1933, Page 21

INTELLECT SHARPENERS All rights reserved.

Eeaders with a little Ingenuity will find In this column an abundant store of entertainment and amusement, and the solving of the problems should provide excollent - mental exhilaration. While some of the "nuts" may appear harder than others, it will be found that none will require a fledge-hammtf to crack them. LOST THEIR ROAD. A party of motorists lost their road after leaving "X" bound for "V," where a weekend was intended to be spent, and tho incident gives the opportunity for a little arithmetical puzzle based upon the details as related by them afterwards. It happened before the days of the. excellent automobile associations, for thero were no finger-posts on the roads to guide the traveller and none of the party knew the exact route to be taken. The mistake in direction was not discovered until the motorists arrived at a place "Z," having driven direct from "X" to that spot. This pl3co "Z" is nearer to their starting point than the intended destination "V"'is, but farther north, the road which should have been followed being duo east from "X." The party learnt upon arrival at "Z" that the "crow-fly" from that point to the road "XV" is . exactly twenty-four miles, but there was only a sheep-track across to it and the tourists were compelled to take the direct road to "V" from the point "Z" where this information was gained. They duly arrived at "V," and after getting some additional information from the people at the latter place which is not necessary for the reader to know for the purpose of correctly answering the question "what is the distance from 'X' to 'V' direct," tho fact that exactly seventy miles had been travelled from "X" to "Z" hence to "V" enabling this to be done? All roads travelled are- perfectly straight ones. TWO ARMCHAIR POSERS. Here arc two little questions involving the simplest of calculations, and provided the reader knows the shortest way to proceed, both should be quickly, answered without the aid of either pen or pencil. A large park containing forty acres is in the form of a square and fenced on all four sides, the respective boundaries running north, south, cast, and west. Exactly in the centre of the park is a small square plot forty yards square with a flagstaff in its centre, and the question is how far is the flagstaff in a direct lino from the northern boundary of the park? Should the reader find more data in this statement than required, he will, of course, see the purpose of it. As is generally known, tho respective freezing points as indicated on Fahrenheit, Centigrade, and Beaumur thermometers are 32.-0.-0. degrees, and boiling points 212.-100, and SO degrees respectively. A simple armchair puzzle from these few facts is what temperature is represented by a Fahrenheit thermometer when a Centigrade instrument shows fifty degrees? And what.would the Reaumur thermometer indicate under these-conditions? TWO CIRCULAR HOOPS. I have two metal hoops circular in shape that once formed part of a whitebait fisherman's equipment, but now with the ends of each joined together forming two circular rings, ono being larger than the other. They are both hanging on the wall resting on the same hook, and their positions prompt a useful little problem requiring the simplest of calculations, for no question of ratio of diameter to circuniferenco or other technicality comes into the matter. As the hoops appear with their circumferences touching only at the point of the resting place, a crescent is formed, the distances between the two circumferences being the greatest at the bottom, namely, four and a-half inches, which means, of course, that the part of the vertical diameter of the larger hoop outside the circumference of tho smaller one is that length. Similarly the distance between the circumferences along the horizontal diameter of tho larger hoop is two and a-half inches. It may be assumed for problem purposes that there is no perceptible thickness in the hoops, and the question to be answered from these few details is what are the respective sizes of the two hoops measured by their diameters? TWO GARDEN. PATHS. :A lady has a plot of ground forty feet by thirty feet which has been formed into a garden containing four equally sized beds with two paths, one running across the plot, the other vertically. The laying out of these paths gavo her gardener quite a lot of trouble in measuring the several lengths and positions according to the lady's specifications, which were that they must bo in the exact centre of the plot running tho full length and breadth, and must be of uniform width, disregarding tho man's suggestion that the proscribed width was out of proportion to the size of tho garden beds. After completion with each of the four equally-sized beds occupying a corner of the plot, the gardener was heard to say to tho cook that the paths took up one-half of the entiro plot, and assuming that that was so can the reader say how wide they must have been? There is a very simple formula for calculations of this character, and this will be published with the solution next week, but whether the reader is acquainted with it or no, ho will doubtless refrain from using either pen or pencil in arriving at the correct answer to this useful little question. "A POSER." The two words "A Poser" are used in a novel way in the following puzzle which, though involving no arithmetical calculation, may give tlio reader a good opportunity of testing his skill. Draw a square of thirty-six cells six by six, or a section of tho chess-board would do, and take thirty-six counters so lettered that six complete p;iir of words "A Poser" can b<s formed with them. The problem is to place as many letters as possible on the board, in any order,' and only one in each cell, so that no letter appears more than once in any direct line, horizontally, perpedicularly, or in either of the two long diagonals. It is obvious at the outset that tho two words as written correctly, cannot appear more than once, and therefore tho whole thirty-six letter-counters cannot be used under the conditions stated. That is whero the crux of the puzzle lies, the aim being to place as many as possible on the board. This will be found quito a difficult feat to perform, and it may not bo giving away too much information if a suggestion be offered to the would-bo solver that the best results aro not obtained by first placing the complete set of letters in as many places as the conditions permit and then filling up the other cells in accordance with' the stipulations, for such method would be likely to leave more empty spaces on tho board than are necessary. \lf the reader can manage to find colls for thirty_»two counters,

the four left over to be different letters, of eom-sc, he will have correctly solved the puzzle.