INTELLECT SHARPENERS.

New Zealand Herald, Volume LXVII, Issue 20620, 19 July 1930, Page 5 (Supplement)

INTELLECT SHARPENERS.

o TRANSPOSING A FIGURE. Br T. L. er.ITOX. A well-known mathematician, Mr. Dudenev, was asked whether it is possible to find a number which can be correctly divided by two, by simply transferring tho last figure to tho beginning. The inquirer was correctly informed that it is not possible. " R.C.," who has invited mv attention to both question and says ho thinks, provided the question mcrelv requires tho result to bo a coirect 'division by two, irrespective 0,. whether it divides evenly or not, that such a number can be found. But that is the point, for Mr. Dudeney's answer clearly assumes that tho number is evenly divisible by two. " R.C.'s idea, however is very ingenious. Can the reader find a number of six different digits, which by transferring the last ono to tho beginning, gives tho same figures in their proper order as _ in the Jesuit of a correct division bv two. Tho number is an odd one, the remainder being expressed as a decimal.

MISS PUTTER AND MISS GREEN. Two friends. Miss Putter and Miss Green, when learning to play golf', decided to stako one penny each on tho result of each round of a serie •• A record of every ono was kept, and at the conclusion accounts wero " squared up.' It was found that quite a large number of rounds had been played. Let it be assumed that at starting, Miss Putter had at her disposal exactly twice as many pennies as her friend had. W hen play finished, however, she had lost twothirds of (he total number of rounds, and one-third the number of pence shi> commenced with, while .Miss Green had then more pennies than her companion, though the sum was one shilling and twopence less than the amount that Ain-s Putter had when placing her ball for the first time on the tee.: Every round was won or lost, there being no draws. JTow much did Miss Green win? BLENDING OF TEAS. The particular grade of tea that si customer required had not been mixed, the prices of the on hand being 3s 4d, 3s. and 2s 4d per pound. The buyer wanted 151b. of a. blend of the three varieties at 3s 2d per pound, stating that he desired the largest quantity possiblo of the most expensive grade put into the mixture. How should his ordnr be made up? TWO CIRCUS RINGS. Two circus rings, one larger than the other, were not concentric, though one was wholly within the other, the two circumferences joining at one part SO that the performers could proceed around either ring from that point. Let it be assumed that these two rings are spherical, and that their circumferences have no geometrical breadth, the smaller circle within the other touching the circumference of the larger at one point, forming a crescent within the latter. A diameter or the larger circle drawn from the point of contact, shows a distance of 9ft. outside the inner circle, and another diameter at right angles to the other, indicates that sft. is the distance between tho two circumferences at each end of the latter diameter. Assuming that the tentpole is in tho exact centre of the bigger ring, what is the difference from the pole' to the edge of that ring ? IN A QUADRANGLE. From a point at a windtow overlooking a quadrangle which is 100 ft. across, a line is fixed 15ft. from the ground, and the other end made fast to the base oi the wall opposite. Another line is fixed on the latter wall exactly opposite the point where the first one is attached, bat only 10ft. from the ground, and similarly made fast to the bottom of the opposito wall. Both lines aro drawn taut, touchsit the point where they cross. How iar is the point of contact from the ground, which is perfectly level from wall to wall, and what height would it be if the quadrangle were only 60ft across? LAST WEEK'S SOLUTIONS. Rugby Football Scores.—Britain, 19. 23, 34, and 19, total, 95: New Zealand, 3. 7, 8, and 6, total, 24. Game of " Soccer."—A against W, 3-0; a-a-'nst C. 2-1; against D, 2-0; W against C. 0 0; against D, 2-0| C against D, 2-1. Motor-car Contest. —144 miles from X, and 162 from Y. Street Collection.—Zones A and B, £350 each; G, £420; and D. £210: tot;.!. £1330. Six-sided Die.—There are six" sides -to choose from when marking the first figure, four when writing the second, ami two for the third. Multiply these and the result is the number of different ways the die can be marked, viz., 48. ANSWERS TO CORRESPONDENTS. " Miss D.B." —Yes, quite correct. " £ s d." —Libra, solidus, denarius. "Flapper."—l cannot say what is tits origin of "flapper" in "the young girl' sense, but possibly the author of the expressive term had " young ducks ' in mind at the time.