"NUTS!"

Evening Post, Volume CX, Issue 137, 6 December 1930, Page 24

"NUTS!"

(B^ t L. Briton.)

INTELLECT SHARPENERS All rights reserved.

Headers with a little Ingenuity ■will find in this column an abundant store of entertainment, and amusement, and the solving of the problems should provide excellent mental exhilaration. While some of the "nuts" may appear harder than others, It will be found that none will require » sledge-hammer to crack them.

MEETING HIS DAD.

A correspondent, C.J.W., says that he delights in a. little problem that possesses sufficient complication without belng'.-toa academic to prevent the would-be-;'/solver from arriving at the correct solution too easity, and in publishing, his poser it may be added inter alia, that that is the aim of-- this column.':,, Here is C.J.W. 's problem. One of the chief delights of little Tommyis to get his mother's permission to walk.down the rather long grassy lane from, the home to meet his dad coming back' in his car from his city office. On one occasion he left at eight o'clock in the morning, returning without any delay whatever, and told Tommy to leave at the same time. He correctly calculated that under these conditions the car travelling uniformly nine times faster than the boy walked, -that he would meet Tommy at twelve minutes to ten. But the boy was ten minutes late leaving home, and at exactly eighteen minutes past nine o'clock he sat down on the grass, where he waited till the car came along. Theao two irregularities of the lad entailed dad travelling an extra two miles before picking up. Tommy, and assuming, as was the case, that the respective rates of travelling were the same as those upon which dad had based his calculation, can tho reader sa.y how far the meeting place was from tho home?

PROVING THEIR THEORY.

Here is another which obscures the correct solution, to perhaps a greater degree than C.JVW.'s problem above. Two sporting ladies attended the annual lacing carnival on Oak's Day as is their custom, and. though both were agreed that one cannot get rich by backing horses, they always made it their prac-. tice on such occasions to demonstrate their theory per medium of the totalisator. Both ladies started out with the same amount of monej*, and after the seventh race they found that, notwithstanding one or two successes, they ■were considerably "out of pocket," one having lost or otherwise spent exactly five times as much as the other, who had then, three times as much left as her more optimistic companion. Miss Prudence suggested "to leave it at that," but was persuaded that they should back a horse to the extent of one pound each in the "Recovery Stakes," the last race of tho day. Unfortunately, the equines they supported were amongst the "also rans," which, for the 'benefit of the uninitiated, means that.they did not earn a dividend. The question, that prompts itself is how much money did the ladies start out with, and this the reader will readily find when-told that the more cautions one had, at the end, exactly four times as much as her friend. Though the problem, is based upon an incident that actually occurred, the ladies require no syjnpathy, as both can'afford to lose, and look upon betting as a luxury, not a, transgression. '

A CHOICE OF ROUTES.

-Before Jones became affluent enough, or rather before he bought a car, he had; to walk to the railway station, to catch- his train daily to the city. Let us have a problem on the distance, not to the station, but to the railway line, which runs parallel to the south boundary of Jones' rectangular section upon which he has built his suburban hipme.'' He can. reach the line by two routes from his front gate, first by walking some distance westward, and then direct south, or by going eastward from the gate to the corner and then the same distance south as in the other route, but that gives him one chain farther to walk. His little boy, however, has, another way, for he takes a short cut, and by starting also at the front gate, he goes the opposite direction, viz.: stranght across the block and over the back fence direct to the line. Now, if the boy's route is only one-third of the shorter of the other two routes, and three-tenths of the longer one, can the reader find the two distances that Jones had the choice of going before the advent of the car. Possibly the reader will find this problem easier than the two preceding ones, for it may be taken for granted than the three routes southward are parallel to one'another. ; •'■■■,

OPTEN ARGUED,

Simple problems not infrequently produce more discussion and argument than, those of a more complicated

variety, and one arising from a recent "dirt track" cycle event is a case in point. A machine travels once round the circumference of a circular track in oxactly three minutes. Half tho distance is travelled at a uniform rate of thirty miles per hour, at "which point the speed is reduced to twenty miles per hour to 'tho end.. The ; question that led to much controversy amongst a group of motor enthusiasts is, what was the average speed of the machine for tho full distance? We will, however, add to that, still keeping the problem in the category of "armchair" posers, and ask the reader to find what is the distance of that track1? He will note, of course, that tho question applies- to any shaped course, a circular track being mentioned merely because the incident occurred on one of that description.

LEAVING THE LID" OFF.

Notwithstanding the abundance of grass this season and the corresponding prolific supply of milk, we still read of the careless vendor who allows water to get into the vessels of the pure commodity, either by "leaving the lids off" their cans when the days are wet, or by allowing the ice to melt and drip into them. Here, however, is an instance where neither of those stock excuses satisfied the Magistrate before whom the case was brought, the defendant being proved to have used three vessels in a systematic process 'of adulterating the milk. One was a fivegallon can, "X,", the other two of unknown capacity, except that one of them, "V," was twice the size of tho other, "Z." He half filled the latter with pure milk, and into "V" he put the genuine product to the extent of exactly one-third of its capacity. After filling both quite full with water, he poured the whole of the contents into the five-gallon measure, and repeated the process three times until the container held four gallons and one-quar-ter. It was while the adulterator was in the act of selling as pure milk the contents of the five-gallon vessel that an inspector luckily "dropped in!" When the reader essays to find what proportion the pure milk: was to the water, he may use as much of the above evidence given by the inspector as may be deemed sufficient.

LAST WEEK'S SOLUTIONS,

By Shadow Measurement. —Eightyfive feet.;.

A Wheel Curiosity.—The explanation ■is that the hub of the wheel, though only making one revolution, to each one of the tire, also progresses or moves along by the carriage of the wheel.

Comparing Their Speed. —Eight and one-third yards.

Another Question of Speed.—Twentytwo and a half m.p.h.; (2) 264 feet.

Wages Paid in Kind.— Twenty-five shillings was the weekly wage if paid in cash. In the particular week mentioned the output was one hundred and forty dozen, of which the employee's share was, at 2s 6d per dozen, £ 1 15s. ANSWERS TO CORRESPONDENTS. ! "Croesus."—Found near Johannesburg,! and its weight approximately is one pound six ounces uncut. The "Kohinor" is smaller. (2) The dimensions are 133 feet "by 85 by 17, but is not completely excavated. (3) The problem mentioned appeared in issue 26th July last. I

P.L.H.—Not merely a question of finding the smallest number. Thanks for interest.

"Old Salt."—Approximately about four-fifths of sea water is common, salt according to one authority.

Correspondence should be addressed to P.O. Box 1023.