INTELLECT SHARPENERS.

New Zealand Herald, Volume LXIV, Issue 19798, 19 November 1927, Page 5 (Supplement)

INTELLECT SHARPENERS.

BX f. I* EBITOW.

Readers aro requested not to send in their solutions unless these aro specially asked for, but to keep them for comparison with thoso published on the Saturday following the publication of the problems.

A CRYPTIC REPLY, A cyclist living at A intended riding to B and returning by the same route. He asked a friend who had a good knowledge of the road how far it was botween the two places, and this was the cryptic way ha received the information. Smith and Brown rode recently between A and B and back on the same track, but not together. From the second day, Smith increased the distance of the rnn each successive day by tho same number of miles, and ro"de to B in four days, and from B to A in one day less, his mileage being increased during each of six days in the manner stated. Brown rode a uniform distance each day, his daily miloago being two miles more than Smith's second day's tally, and the journey there and back took him eighfb days. The speaker's method of reply was enjoyed by his friend, who was a problem-lover, when tho " nuts" were, like this one, not difficult. Can the reader determine tho distance between A and B ?

ANOTHER NOVEL FOOTRACE. A novel footrace took place recently, which was reminiscent of the famous one between tho cook and the gardener. But, in tho present problem, there is no need to take anything for granted, as all necessary data are set out. There* were in the race a hefty youth Bill, a mediumsized lad Max, and a smaller boy Sam.AH started together off scratch, each boy taking different-length strides, but uniform throughout. M's were half as long again as Sam's, B's two and a-half times the length of the latter's, and one and two-thirds as long as those Max took. Now Sam took three strides to every two of Max's, and five to every two that Bill took, while the latter ran three for every five that Max made. The track, less than 100 yards, was marked m one footlength, and, assuming that during the race the two smaller boys hit the same marks together twenty-five times, Sam and Bill fifteen times, and Max and Bill ten times, what was th» distance of the race, and who won ? Each boy landed on the winning-post mark, even if the last strido was not tho prescribed length.

"TWO AND TWO." The expression is frequently heard that " two and two equal four all the world over," being generally used to > emphasise that a point in an argument is unanswerable and beyond cavil. But why two and two have been chosen for this idiom is due, no doubt, to the fact that those numbers produce the same result whether they be added together or multiplied. Whether that be the reason or not, however, does not alter the fact that there are many other numbers which possess this feature. There is an invariable rule which will enable them to be found. Can the reader discover two numbers having this peculiarity, not necessarily the same number repeated, as in two and two?

TILE PAVING. One often sees, when floors of new buildings are being tesselated, that tba workmen are obliged to cut many o! the tiles, in order to fit exactly into the spaces along the sides and in the corners. No doubt there are excellent reasons that the areas to be paved are not designed to conform to the standard sizes of theso paving slabs, for certainly the cutting and patching does not add to the beauty of the floor, however neatly the work be done. And it is not the easiest of calculations to determine the least number necessary to be cut so that there is no waste. A nice little problem is suggested by this. A square floor about to be paved had a superficial are 3 equal to the aggregate measurement of twenty-nine square tiles, all of uniform size, which were to be used for the job. As twenty-nine is not a square number, obviously some must be cut and fitted. Assuming that there was no waste, and that no tile was cut into more than two pieces, what is the largest number of whole tiles that can be used in the job 1

THREE PADDOCKS. A surveyor had completed the measurement of an area of land for a glazier, who intended fencing them into three separate blocks, the largest to be used as a. lambing paddock, tlio next weaning, while the smallest was intended for a horse paddock. According to instructions, the surveyor had measured them in the form of three squares of different areas, the common difference being 72 acres. On looking over the plans, the grazier said that the lambing paddock was not large enough, whereas the other two were each bigger than he required them. As no new land was to be measured, how much should be taken off the lengths of the sides of the two smaller paddocks, and by how much should the length of the boundaries of the large paddock be increased, so that the areas will, be 250 acres, 160 acres and 90 acres, each paddock retaining its square form ? LAST WEEK'S SOLUTIONS. Sheep Pens. To construct a pen witbi thirty-two hurdles, so that 640 sheep and no more could be yarded, allowing each animal one and a-half square feet space, fourfee fc hurdles would do, if the yard were made ten hurdles by six. Competitors In Partnership. A, with 12 points, was Y's partner, who gained 6. B had X as her companion, each with nine points, while Z obtained 30 points, just double the number scored by his partner, C. A Point on the Circumference. The diameter of the circle within the rectangle must have been ten feet. If there had been no limit to the size of the rectangular figure, another circle could have a diameter of 58ft.. on thu figures stated in the problem. Darby And Joan. The conversation must have taken place t in 1926, Darby's age then being 4b and 1910' S Darb Y junior was born in Dominoes Problems. There are only three other arrangements S\ Dg °i> <? five, viz -(1-0), (Oi-Oj, (0-2), (1-3), the second example similar, except that the two end dominoes are (4-0 L (1-0). The third arrangement is (2-0), (0-0), (0-1), (1-3), (3-0). To total six with five dominoes there are ten different arrangements. ANSWERS TO CORRESPONDENTS. Mac Spar.—(l). There is no definite record of the number of languages in th« world as distinct from dialects, owing ta the fact that philologists are divided on the question as to the point at which a dialect becomes a language. Up ta December 31, 1926, the B. and F.B. Society ha.d translated the Bible into 59*. defined languages, and it is roughly estimated that this number represents about seven-tenths of the total. (2). Wit in the Papua zone, extending approxmia y 100 miles around British New Guinea, there are 83 distinct ianguagos and near j 200 dialects. (3). The Un:t«J Kingdom has five separate tongues, viz., Eg Gaelic, Welsh, Erse and Manx. soyssu. Septento J , ing. J'hanks for your lasi*