INTELLECT SHARPENERS.

Otago Daily Times, Issue 20290, 24 December 1927, Page 19

INTELLECT SHARPENERS.

By T. L. Beitox. Readers are requested not to send in their solutions, unless these are specially asked for, but to keep them for comparison with those published on the Saturday following the publication of the problems. CHRISTMAS BREW. An old lady brewed a quantity of hopbeer and parsnip wine for Christinas family use. There were 50 gallons altogether, which were contained in six 10-gallon casks. All of the casks held-different quantities, and none of them was full. The chalked figures on the outside of the kegsgndicated the number of gallons each contained, viz., 3i H, 4|, si, 55, and 6—but in all respects the barrels were outwardly similar. The hop-beer was for the three sons and their families, the wine being kept for the old dame’s household. Hiram's and. Joshua’s families lived together in a largo house, and their combined families numbered twice that of Reuben, who ' lived in a small cottage nearby. The hopbeer was apportioned to the families on the basis of the same quantity for each member, irrespective of ago, and Reuben did not forget to remind his mother that his mothcr-m-law was expected down for. Christmas. This being remembered, it was found that tho beer could bo sent to the families without interfering in any way with the contents of the kegs, so that each member of the three households, including the dame’s, had the same quantity of tho brews. How many participated,, and which keg held the fermented juice of tho root plant? The dame’s household numbered two-fifths of the combined families of Hiram and Joshua. AMATEUR ENGINEERS. Two roadmen, ambitious to become contractors, secured a drainage job from a county council. They had not much k >wledge of figures and estimates, but uero good, practical men in road work. E rom the specifications of their new contract, they wrote down the official estimate of the maximum volume of storm surface water that would have to be carried away by the cement drainpipes, but they could not agree about the size of them. They therefore took the official figures to the local schoolmaster and asked him if the pipes they had in mind—6o inches in circumference —would do. Tile pedagogue made the necessary calculations for the men, and told them that drainpipes of half the capacity of those mentioned would carry off the water indicated by the’ figures, and leave a safe margin. ’The men thereupon put down pipes 2ft 6in in circumference, but tho first heavy rains, though the volume of water was less than estimated, proves! that tho pipes were too small. As the schoolmaster’s calculation was correct, where was the mistake?

IN A COUNTRY STORE. Business .at the counters of a general store in the country was very slack one day recently. An occasion of the kind afforded opportunity for the hands to prepare for busy hours. On this day the manager, knowing the healthy rivalry existing between two of his apprentices who were in different departments, set them to work, the one weighing tea in lib packets, the other cutting one-yard-wide towelling in 18in lengths. The manager decided that one length of towelling could.be cut in the same time—4s seconds—as two packets of tea of lib each could be weighed. On this basis the apprentices started together, one with a roll of 18 yards of towelling, the other with a 601 b chest of tea. Halfway through, the grocer was interrupted by customers for three minutes 45 seconds, but the draper’s boy went through without stopping. How efid the contest end in point of time, and who won, allowance being made for the interruption to the grocers apprentice? Of course, it is assumed that the boys worked uniformly with the time estimated by the manager. One little, but vital, point in this is liable to he overlooked.

A PECULIAR NUMBER. Here -is an arithmetical curiosity that is worth investigating. There is a number consisting of eight separate digits (that is to say, no figure in the number repeated) which, when multiplied by any single figure called for promiscuously, and multiplied again by any figure the operator desires, will yield a result that will be a repetition of the number called for. And further, these repeated figures if added together will equal the product of the multipliers. The eight digits in the multiplicand are in consecutive order, > with one omission, and the only condition attached to this curiosity is that the number called for, or suggested by anyone not demonstrating the feature, must be one of the eight. If the eight figure number is unknown to the reader its discovery will require quite a lot of’ thinking. Both the single numbers used as multipliers must bo also in the multiplicand.

HARVESTING HAY. Sheep farmers do not as a rule go m for extensive hay growing, and therefore do not have the necessary equipment for harvesting the little quantity that is grown, even if their ordinary sheep men could be spared for the work. Contractors are generally given this job, and usually accept payment on a percentage basis of bales harvested. Supposing a contractor agreed to harvest a crop on the understanding that he received one bale in every three bales harvested, and that just as the work was completed, heavy rains caused one-ninth of the total, which had been stacked in the low part of the field, to be spoilt for feeding purposes, and supposing also that after retaining 76 bales of good hay for his own stock, the contractor could' only sell 308 bales to the produce merchants, what was the total number harvested? There is just, a possibility of this simple problem tripping the unwary.

f LAST WEEK’S SOLUTIONS. \ UNDER DIFFERENT CONDITIONS. I The wind must have been blowing on the L outward and return journeys at 30 miles I an hour. Therefore in calm weather with f the engines working at the same speed f uniformly, a straight flight of 400 miles L would take eight hours, the time occupied > in flying 160 miles against a half-a-mile-a-minute wind. I “BRING AND BUY."’ The number of married women taking £ part in the sale of violets was 48, and of unmarried 16, a total of 64, who each V bought 5s 3d worth. A QUEER FORM OF LEGACY. The largest possible amount under the conditions is £304 Is, the sum being: £206 0 5 8 0 7 £304 1 0 in which all the digits and the cipher appear once only. AN OUTBACK RAILWAY. The distance from X to Z must have been exactly 100 miles. Under the conditions set out there was no stop at Y, the reduced speed making the train therefore half an hour late at Z. CURIOUS FIGURES. Eleven, twelve and thirteen arc the three J consecutive figures. The two latter multiJ plied together added to the former make 167, and as stated in the problem 168 is one loss than 13 squared. ANSWERS TO CORRESPONDENTS. S.M. —Frost’s publication refers to Frcn--1 ido and Bergholt. and acknowledges their worth. j P.S.N. —The 11 “moves” have been | posted in your addressed envelope. P.l.ll—Published last month; see issue j of November 26. 3 W.T.—The area according to the particuj lar= stated, was limited to the glass only, the woodwork being ignored, j J.H.S, —Whether money-lenders’ practice is to deduct the first interest before handing I over the amount of loan is not known, but j that happened in the problem, so the conI trary cannot be assumed. j “ Curious.”—Thanks for your “curious” ) explanation. Intend going into tho matter 5 at first opportunity, but. prima facie tho I “ freak ” has no support in mathematics.