INTELLECT SHARPENERS.

Otago Daily Times, Issue 20400, 5 May 1928, Page 19

INTELLECT SHARPENERS.

at ;. By T. L. Beixox 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. THREE INVESTMENTS. A sum ol £ISOO was subscribed by three investors—Atkins, Beggs, and Carter—for the purpose of providing the capital for a little venture in New Zealand tobacco culture. Atkins invested £250, Beggs £SOO, and Carter £750, and the terms of the joint enterprise were that all net profits should be divided in such a way that the rate of interest that each received would be in proportion to the amount invested. The venture turned out successfully in the first year the net profits for that period'being £245. How much should each receive ? The reader should fully understand the question before proceeding to solve it, as it is liable to catch the unwary. AT THE BARBER’S. While waiting my turn at the barber’s the other day an incident occurred which at once suggested a little problem. There were four others in the room besides myself. Our hats hung together in one row, and the first gentleman to leave inadvertently took another’s hat, but Ijimeelf discovered the mistake before reaching the door. Now, the five hats were identical fn every way, as these certainly appeared to be, and that each owner took one at random, what are the chances that everyone took a hat that did not belong to him? This is_ an interesting little problem, and there is a very simple rule for solving it, but the reader not acquainted with it will perhaps get an idea of the rule from the obvious fact that if there were three men and three hats, the chances of everyone taking at random the wrong one, would be only two. A MATHEMATICAL PARMER. Generally speaking a farmer has very little time in which to study anything outside his business. People, however, wso travel much in the rural districts and become personally acquainted with these captains of primary industries, have remarked how frequently well informed and keenly intellectual men are to be met in this circle, some of whom have perhaps not enjoyed the benefits of an education as advanced as others. An excellent example of the type that _ has done so well without a university training was met recently, and an ordinary question as to the number .of sheep on his station brought forth a reply that revealed an extraordinary aptitude for figures. “ All my sheep,” he said, “are in five paddocks, and, curious as it may seem, two-thirds of those in the wool shed paddock, five-sixteenths of the number in the block, adioining, two-sevenths of the total in the third paddock, five-sixths of those remaining on the ‘ creek ’ section, and two-fifths of those in the mountain paddock are the same number, there being between 20,000 and '22.000 altogether.’’ Can tho reader find exactly how many sheep he had and the number in each of the five paddocks? WHICH WERE THE TWINS? Here is a problem that may be found at first to be a little more bewildering than the usual example of age puzzles. The solution is, however, easy to find by algebra, though the reader will enjoy more mental exhilaration from it, as well as some fun, if simple arithmetic be used or methodical trials. Some years ago there were only three children in the family, viz., A, B, and C, whose combined ages were exactly one-half that of the mother. Five years later, during which period another child-, D, was born, the total ages of the children just equalled the mother’s. During the following 10 years yet another baby, E, arrived, and on the day of its advent A was as many years old as C and D were together, and B three times as many years as the two youngest children. At the end of the ten-year period mentioned the mother’s age was only one-half of the united ages of tfio children, and B’s and C’s combined ages were then only three years less than hers. It follows that if the age then of one of the three eldest children exactly equalled the combined ages of the two youngest, as it certainly did, two of the former must be twins, and the problem is to find which they were and also their age when the youngest child was born. NOT BY SUBTRACTION. “Puzzled’’ writes:—“Would you please help me to solve the following problem, No. 6, Section 16 of Baker and Bourne’s Algebra, as 1 and my friends get an answer different to that in the book?”. The problem is: Find the excess of one of the following expressions ■' over the other,” viz., 2 (a-b) and minus 2 (a-b). “ Puzzled ” adds, “in other words, subtract one from the other.” I have not the text book by me to verify the question, but it does not seem that the correspondent has correctly stated it, otherwise he should not be puzzled to find the correct answer as published by Baker and Bourpe. More probably the question is to find by what part of one expression is the other in excess of it? For example, if one were asked by what fractional part does eight-eighths exceed seven-eighths, the solution is not one-eighth, obtained by subtraction, as that would not answer tho question. The correct answer is oneseventh, because one-seventh of seveneighths is one-eighth, tho actual difference. Perhaps “ Puzzled ” will look into his oroblera again in this light. LAST WEEK’S SOLUTIONS. ‘ SHOP SALES. " If an article be marked at 35 1-3 per Cent, above cost, and reduced 10 per cent, on selling price, the profit is 20 per cent., not 23 1-3 per cent, as it might appear to be. The cost price of the article sold for 12s would therefore be 10s. AT TWO SPEEDS. The average speed was 24 miles per hour, indicating that the distance of tho track was 1 1-5 miles though no doubt some readers made it 1* miles round. ANOTHER DEAL IN BROAD ACRES. The farmer who had 6000 acres should get £BOOO out of the £IO.OOO, whilst the one with 4000 acres would be entitled to £2OOO only, paradoxical as it may seem. ADDED WATER. Tho adulterated milk contained 11-18 of added water, and therefore only a little more than one-third of pure milk—five gallons of this mixture would contain 3-1/12 gallons of water. THE PROFITS OF ADDED WATER. The vendor who adulterated the milk in the manner stated made a profit of 60 per cent., or £5 16s for the week. ANSWERS TO CORRESPONDENTS, p. P. R.—Neither player can win except by the bad play of his-opponent, so every game should be a draw. R. G. A. —Yes, it is quite possible for a cube to be passed through another cube of smaller dimensions. It will be ex plained in a problem shortly. “ Cheerio.’’—-Thanks.