INTELLECT SHARPENERS.

New Zealand Herald, Volume LXIV, Issue 19833, 31 December 1927, Page 5 (Supplement)

INTELLECT SHARPENERS.

int ft. x» aamfti, j Readew «:e requested not to lend ¥i\ j their tolutioHM -unless thes« are fipecially j asked for, but to keep them for compart I son -with those published on the Saturday * following the publication of the problems*. 1 1 % SEVEN (JOINS AND CQTTABE&, A cardboard square, like otj ordinary ■ draught board, but containing only 16 spaces, was placed on a table; in fact, ; several of them, with an abunlincoof j counters representing . the :following values, viz:—6d, lii, 13 6d, 2s ( 2s 6d, j The problem was to place not more than j one counter on a square, so that tho j largest possible sum would bo shown, j on the board, the only condition being ; that not more than one counter of the ' same value should ho in direct line, pev- ' pendicnlarly, horizontally or diagonally. ; It is not necessary that every space be j occupied if bettor results can be obtained j otherwise. This will provide excellent j mental relaxftvi<?a after bwiaess worries, „ | or, say, after & too-close study of the motor regulations. Tt is rot i) 3 simple, j however, aa for there ia a psl> \ fall ia it. i NEAB TEE ASSOUAN DA2IL j The authorities have jurt completed 9 | survey of 804,24) acres, 2 roods, 16 per- ' j ches of land for irrigation purposes near <■ the Assouan Dam, which, it is predicted, i will be the largest and most productive, j compact block artificially watered in the world. For calculation purposes, these figures are not formidable, as the several distances which concern this problem are j in simple numbers of miles. The area is circular, with a circumference of 125.6641 ■ miles. At 9 o'clock one morning, an Arab started to walk from a point 6 2-3 miles due south iron the centre of tie r area, and at the swne -time a Bedouin, left a point on the circumference d«& west of the centre—where a well was situated—to walk to that place direct. At 10.40 a,m. he arrived at a village 15 miles west from the well, and aft that time exactly, the Arab reached it. Both rested at their respective places for twenty minutes, when B continued walking direct to the well, A proceed- j ing direct to meet a chain-man at "a hut on the circumference due north of i the well. The latter, however, had left th<s hut—also at 11 a.m.—walking direct . to where B had rested. Assuming that each man kept hi 3 own uniform spe.'d, 1 and that A reached the hut, B, the j well, and C, tha village, at exactly 4 'f p.m., at what rate did each walk?, y A FIELD 03? OATS. A farmer, with his three sons, worked night and day, two in each shift, in order : to harvest a field of oats, while the ' weather and the moon were good. As | there was only one mower, they agreed that two men together were sufficient, and that those on day-work should cut , as ns-ir as po.'saible half as much again as the other two. The field was oblong in shape, the length of the sides being as four ii. to three i The first day they cut a strip twelve yards wide from the. ] fence all round the field, and that night the other two mewed in the same manner a strip eight yards wide. Next day an additional fourteen yards wida were cut round the field, line night-workers doing more than their quota, viz., a l strip ten yards wide. The total thus cut was exactly half the field, and, assuming that tlie oats jrrew tight up to the fence all round, what w is tho area of the paddock? " ' THE SAME BLOCK OF LAFD, Another problem equally aa brain stimulating as the. previous one is suggested by the same field of oats, though the problem involves the reverse method of calculation. Supposing that the men, dnrinr; those two days and two nights, were able to cut only on area of 5 acres j and 32 perches, in the same form as in the previous problem, what width would ! they have cut around the field ? The -32 perches are : nc;udod to avoid involving fractions in the calculation. Both : of these problems aro very practical ones. ' , AT AN EATING-HOTTSE. Six friends came down from the country for the Christmas holidays, and although they had sleeping accommodation in different parts of the city, they selected a first-class eating-house, and decided to take all their meals there during the visit. They could not, however, secure one table for the whole party; in fact, they were glad to take the only ones available and reserve three, each capable of only seating two people. They arranged that no two should sit at the same table together more than three times, and that everyone should sit at three meals with each other, the duration of their visit to end when this arrangement had been carried out. Assuming that the visitors partook of three meals a day, starting with breakfast on the first day, how long did they remain ? Another problem of " combinations" will be published next week, but not quite so easy as this one, LAST WEEK'S SOLT7TIONS. Amateur Engineers tfhe schoolmaster was correct, as h«\ told the men that pipes of hi If the capacity of those 60in. in cirejff.lere-.ica would leave an ample margin tf safety. But the amateur engineers thought that pipes half the circumference wonld be allso half the capacity, hence their inability to carry off the water, the volume of which was much less than estimated j for, as the reader knows, their capacity would only be one quarter, not ono half. -In A Country Store. The contest ended in a dead heat. Eighteen yards (or 54ft.), cut into one foot and a-half lengths, would require 35 cuts, not 36, which, at 45 (seconds each, would take 26 minutes 15 seconds. Ona 21b.-packet of tea, weighed in 3 of a minute, would permit of the 601b. being finished in 22£ minutes, which, added to the time lost, via., 33 minutes, would make the actual finish of the contest a tie., A .Peculiar Number. Hie number is 12,345,679, for, if it be multiplied by any single member of the eight, and the:, by nine, the result will be a repetition of the former number, which, added together, will total the product of the two multipliers, e.g., 12,345,679 x2x 9 = 222,222/222, and these., added together, total 9x2, via., 18. Harvastiag Hay. The total number of bales, harvested was 1296, of which 144 were destroyed. The contractor's share was therefore 76-f3o3+one-third of 144 =432. _ ANSWERS TO CORRESPOND Elfr& Radio: "~Th«j idea of propoundfccf m wireless problem has aot b* oll " K.H."— Practical prcbleto more tin jrogu® in sehijol ntathtana^