NUTS TO CRACK.

Otago Witness, Issue 3870, 15 May 1928, Page 17

NUTS TO CRACK.

By

T. L Briton.

(For the Otago Witness.) Rexd«r» with a llttl* Ingenuity will find In ils column an abundant atera of entertainmer * and imuwaaant. and ths 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 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 the publication of the problems. TWINS AND “SUMMER TIME.” Some one has suggested the possibility of legal complications occurring in cases where twins were born on the night of March 4 last, or rather, in the early morn of the sth, at about the time the hands of the clock were put back one hour. Let us take a hypothetical case. When Mr Hopkins made his will leaving £9OOO to his heirs and assigns, he was aware that his wife would, in the natural order of things, soon present him with their first-born, but did not overlook the possibility of twins. In this event the will provided that the money should be divided in the following proportions:—Half to the widow, one-third to the first-born, one-sixth to the other twin, and one-ninth to an orphan niece. Twins were born on that eventful morning. Jack’s arrival was at 10 minutes to 2, just a half hour before Bruce. How should the money be divided legally between the twins, it being of course understood thatsummer time ended at 2 a.m., and that all clocks were altered in the prescribed way? The reader will note that the fractions indicating the allocation total more than one whole, or unit, but the problem explains this. THE COST OF YARDS. A farmer had a flock of 1764 ewes and..-wethers, the former numbering 1134 and the latter 630. He arranged to have*a number of small yards erected to be ready for shearing time, and required each yard to contain the same number of animals, each class being kept separate. He found that the lowest cost for erection of the required number of yards, each capable of hold-, ing the largest number possible, under thees conditions, would be £BB 4s, and asuming that the price of the yards was the same in every case, what did they cost cacn? This useful problem is not difficult provided the reader follows a proper method of calculation, otherwise it is quite possible for him to spend unnecessary labour in trials. NURMI, ROSE, AND HAHN. A novel way of testing the comparative speeds of long-distance runners was introduced recently by the supervisor of one of the athletic clubs. Being a strong opponent of the “time tests,” he successfully Worked out a scheme for ascertaining the relative speeds of his men by a “ distance ” theory on a circular track. Perhaps a little problem will show his method. Nurmi, Rose, and Hahn were known to be able to run in a given time 848yds, 714yds, and 504yds respectively, and a trial of the three champions was run uniformly at these speeds on a circular track a quarter of a mile in circumference. Assuming that they started off together and stopped when they were together again for the first time, how far had each man run, when they finished t x By such a test it would seem that a trainer of athletes could obtain a better criterion

of his men’s capabilities than by the orthodox “ time ” trial. GRASS RIGHTS. Tn what was known as the “ way back ” country in Australia, where the rainfall is precarious, a large business is done in good seasons between landholders and owners of' stock in less favoured districts by selling “ grass rights.” For when rain comes the arid plains give place to grass, trefoil and other edible growth in a night, and an abundance of feed comes and disappears so rapidly that there would be a large wastage if additional stock from outside were not brought in. A grazier had a small 10-acre paddock of uniformly growing grass, which he knew by experience 17 horses would eat off in 30 days, and 19 horses would exhaust in six days less. He sold the grass rights for £lO 8s for a period of eight days only, as the paddock was required to be then spelled for sheep later on. Can the reader determine from these facts how many horses could be grazed for eight days (and the cost per head) so that the growing grass would be exhausted exactly at the end of that time, on the assumption that four of the horses were withdrawn at the end of six days? It may be inferred that all the horses are of the same feeding capacity. TAXATION. Demands for payments of taxes whether they be in respect of income or for municipal services, convey more practical information to the average taxpayer when they state that the amount claimed represents so much in the £ then when the sum is quoted as representing so much per cent., for 6d in the £ is more understandable by many people than 2J per cent. _ A merchant whose accountant handed him a statement showing that income tax, life insurance and similar personal obligations represented 3s 2d in the £ on his income,, found, after paying these dues, that he had £1969 10s left, his total expenditure for the .year under all heads leaving him -with a net credit balance of £B5B. How' much in the £ did his total annual expenditure represent? - -7 LAST WEEK’S SOLUTIONS. THREE’ INVESTMENTS. The respective profits for the year of the three investors Atkins, Beggs and Carter, were £l7 10s, £7O, and £157 10s. AT THE BARBER’S. With five hats there are 44 chances that the five owners 'would take hats that did not belong to them assuming, of course, they were taken at random. WHICH WERE THE TWINS? B and C were twins and must have been nine years of age when the youngest child was born, the mother being then 30. A MATHEMATICAL FARMER. The farmer must have had 21,539 sheep altogether, and the numbers in each of the five paddocks were:—27ls, 5792, 6335, 2172 and 4525. NOT BY SUBTRACTION. Seven of anything if increased by one seventh will make eight, and the example quoted was not a sum in subtraction. ANSWERS TO CORRESPONDENTS. F.L.—There are several interesting points involved—First of all one of them must end in the second row, though that was not stipulated. And again the first part was confined entirely to the square. Thanks for your interest. P. L. H. —Just a question of finding the smallest number.