NUTS TO CRACK.

Otago Witness, Issue 3869, 8 May 1928, Page 16

NUTS TO CRACK.

By

T. L Briton.

(For tub Otago Witness.) Rexdtra with a little Insanulty will find in ile column an abundant ■ter* of antertainmei' and amusement, and the solving of the problems should provide excellent mental exhilaration. While some ot the "nuts’ may appear harder than ethers, it will be found that none will require a sledge-hammer te erack them. Solutions will appear In our next issue together with some fresh nuts.’ 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’ tho publication of the problems. three investments. A sum ol £l5OO 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 £5OO, 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 himself discovered the mistake before reaching the door. Now, supposing the five hats were identical in 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 tho wrong one, would be only two. A MATHExMATICAL FARMER.. Generally speaking a farmer has very little time in which to study anything outside his business. People, however, who 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 j 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 thaC 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 Irom it, as well as some fun, if simple arithmetic be used or methodical trials. Some years ago there were onlythree 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 tnc 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 followilig problem, No. 6, Section 16 of Baker and Bourne’s Algebra, as I and my friends .get an answer different . to that in tlue 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). adds, “in other xvQTds, 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 publish 1 by Baker and Bourne. More probably the question is to find by what part of one expression is the other in excess o f it? For example, il one were asked by what fractional part does eight-eighths exceed seven-eighths, the solution 13 not one eighth, obtained by subtraction, as that would not answer the question. The correct answer is one6?ve’\tiL . because one-seventh of . seveneighths is one-eighth, the actual different Perhaps “ Puzzled ” will look into his 'iroblem again in this light. ’ LAST WEEK’S SOLUTIONS. SHOP SALES. “ If an article be marked at 33 1-3 per cent, above cost, and reduced 10 per cent on selling price, the profit is 20 per cent.’ r ot rrT 1 ’ 3 per cenfc ’ as ifc mi gbt 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 the track was 1 1-5 miles though no doubt some readers made it miles round. ANOTHER DEAL IN BROAD ACRES. The. farmer who had 6000 acres should get £BOOO out of the £lO.OOO, whilst the one with 4000 acres would be entitled to £2OOO only, paradoxical as it may seem. ADDED WATER. The 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 50 per cent., or £5 15s 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 cubs of smaller dimensions. It will be explained in a problem shortly. “ Cheerio.”—Thanks.