NUTS TO CRACK.

Otago Witness, Issue 3829, 2 August 1927, Page 17

NUTS TO CRACK.

By

T. L Briton.

(For Tins Otago Witness.) Readari with a little ingenuity will find in ils column an abundant •tore of entertainment and amusement, and the solving of the problems should provide excellent mental exhilaration. While some ot the "nuts", may appear harder than others, It will be found that none will require a sledge-hammer to crack them. Solutions will appear In our next issue together with soma fresh “auts.” Readers - re requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published in the issue following the publication of the problems. BLENDED TEA. Problems involving weights and measures are always interesting because practical, and because they are met with in some form or other almost daily. A tea merchant, noted for the many differentlypriced blends he kept in stock, had a lady customer who invariably desired a mixture costing a trifle more or a little less than those ready for immediate sale. On the last occasion the prices of the teas then iu stock were as follows:—3s 4d, 3s, and 2s 4d per lb. But the ladv would be satisfied only with a blend of the three varieties at 3s 2d per lb, of which she ordered 151 b. In blending the teas to make it cost this price at the rates quoted the merchant gave her the smallest quantity possible of the best tea at 3s 4d per lb, as his profit on this kind was less 1 “ ian others. How should the lolb be mixed under these conditions? A MATTER OF DEGREE.

It was a wet day, and two visitors were weather-bound in a small backblock town during a recent week-end. The hotel was without a library or similar distraction, and Hopkins suggested a game of cards to pass away he time. Tomkins would not play if the stakes were high, as he did not gamble. Everything, he said, was a matter of degree, and playing for low stakes, when the players could afford to lose, was in no sense gambling. They played, therefore, for shilling stakes. Tompkins had, to start with, three times as much money as Hopkins, and when they had finished the latter had lost two-thirds of what he had, while Tompkins had £24 12s more than three-quarters of what Hopkins had left. How much did Tompkins win?

A NOVEL COMPETITION. There was a novel walking competition between two members of a certain club. It was a long distance walk, and the novelty of it was that each started at a different end of the route, one at A and the other at Z, and they walked to meet each other, which they did at X. The weather was excellent and thousands either followed or watched the competitors; who started simultaneously from their respective marks The full distance from A to Z was 51 miles on a straight road. B, starting from A, walked uniformly at four miles an hour and rested for 15 minutes at the end of every five miles, while his adversary Y,’ walking at a uniform rate ot live miles an hour, rested for 24 minutes in every five miles. On the assumption that their rates of walking, as well as their resting times throughout, were as stated, how far was their meeting place X from the two starting points? NUMBERED CUBES. Suppose, that a cube is marked on its respective sides 1,2, 3,4, 5,6, and so numbered that any two opposite sides add up seven—for example, 6 opposite 1, 4 opposite 3, and 5 opposite 2, these forming the only combinations of two of the numbers that will make seven. There are six

sides to the cube, and if we mark one side with a unit and the opposite face with a 6 it. must be remembered that there aro five other sides of a blank cube upon which each of these two figures can be marked; and similarly with the other combinations mentioned. Now it is a nice little puzzle, yet not a difficult one, to find in how many different ways the six figures can bo marked in the manner stated. POSTAGE STAMPS. The postage staihp desks at a post office present, practically at all times of the day, the busiest “shopping” centre in a city. But if one arrives there shortly after opening time the'clerks have time to say “Good morning,” to their friends. A gentleman the other morning had just received one shilling’s worth of penny stamps from the clerk. TJ \v were in block form 3x4, and as he picked them off the counter he asked the lady vendor in how many different ways could four stamps, all joined together, b.e torn off a 3 x 4 block such as he held in his hand. He added that they must be properly joined on, at least, one whole side, and not merely stuck or hanging by a corner. The clerk immediately answered 12, but by the look of the gentleman’s face it could be seen that 12 was not" the answer, though he did not enlighten her. I looked into the matter that evening, and found an interesting solution of such a simple and innocent question. Can the reader find it, too ?

LAST WEEK’S SOLUTIONS. ' r; WEEK-DAY CHARITY. In ordinary years beginning on a Sunday the lowest amount that could be distributed on week days in the manner stated is £19,345. As 1928 will be leap year the smallest sum would be £69,174, giving £221 every week day with £1 left over after the las’, dole on December 31. FOOTBALL SCORES. Wellington v. Auckland. 2—o; Wellington v. Canterbury, 0 —0; Otago v. Canterbury, 2—l; Otago v. Auckland, 2 —o; and Canterbury v. Auckland, 2 —l. The problem stated that Otago beat Wellington, 3—o. THE CHEESE MERCHANT. There re exactly 42 different ways that the cheeses could be arranged on the shelf in two equal rows, the lightest being on top, and every cheese being of less weight than its right-hand neighbour in each separate row. IN A BOARDING SCHOOL. The fewest number of occupants of the eight dormitories under the stated conditions, each apartment being occupied on every night,..would be 32. A WEDDING GIFT. The office subscribed £7, the commercial travellers £8 Bs. salesmen £4 4s, and the packers £7; —total, £26 12s. ANSWERS TO CORRESPONDENTS. W. M.—“ Fixed prices” correct. Something similar to the 17 horses has already appeared.—Thanks. R. C. —The solution is mathematically the same, but the figures as given conform more nearly to practical conditions and therefore are more suitable for this column. S. A.—-The number of men was, of course, the same at the two tables—viz., six and four at the first sitting, and five and five the next. But the goods purchased the first time included two items more than on the second occasion, hence the Is extra. J. B. —Your letter received. The paradox was explained in the issue of July 19, as you will have now seen. erratum. The end of the solution of problem “At fixed prices” (July 19) should read "if the number were 100 and not 200 there would bo only one possible way—viz., 19—1—80.