Intellect Sharpeners.

New Zealand Herald, Volume LXVIII, Issue 21030, 14 November 1931, Page 5 (Supplement)

Intellect Sharpeners.

BY T. £. BRITON.-

SAVING THE CHERRY TREES.

Owing to the low price of eggs and the difficulty of profitable export, a poultry farmer who had a three-sided block for liis fowl-run, decided to sell his poultry and grow cabbages for the market. The three corners of the section formed by the boundaries* were each less than a right angle, making the block more difficult to plough without waste, so he decided to take the fencing down and fence the land, or as much of it as possible, in a block oblong in shape. But there was a bearing cherry tree exactly 30 yards from the south-eastein corner, C, as well as four others just coming into bearing, situated 12ft. apart, but closer to the corner mentioned than the tree f.rst referred to.The lengths of the sides are: A.8., six chains and eighteen yards; 8.C., six chains and eight yards; A.C., two yards less than six chains. The question is how much of Die original " run " will be cut out by omitting the cherry trees, in order that the largest possible oblong block can be secured with the five trees fenced out!. ECONOMICAL FENCING. Here is another useful problem upon the same theme. A square piece of ground is fenced on all four sides, the total length being 176 yards. The surrounding lands, all unfenced, belonged to the same owner. It was decided to enlargo the fenced portion, but not to alter the square shape of the block when enclosed, and as economy was the watch-' word with the owner it was decided to use to the utmost, as much of the old fencing and gates on the original block as possible. At the same time he utilised all of it that was found to be on the new boundaries, thus saving some removal and re-erection, this being possible notwith* standing that the proposed larger block" comprised additional land, extending beyond the four boundaries of the small section. The point is to find what is the minimum length of extra fencing that would be required to fence in the largest square area possible under these conditions, f.Il present fencing that can be used without removal to bo retained in its original position, which must include the four original corner posts. Gates, etc., are assumed to be " fencing " for the purpose of the problem. PUZZLING ABRANGEMENT. To solt'e this apparently simple little puzzle by H. E. Dudney, may possibly tax the reader's ingenuity more than his knowledge of arithmetic, and it may also require o:i him a good measure of patience. There is no rule or formula to assist him, as far as the writer is aware, so he needs must unravel the mystery by trials, ia which case he may be lucky and strike the solution at first attempt. But let the trial:; be carried out by some methodical system, and much more enjoyment will be got out of the puzzle. Threaded on a string are ten Chinese " cash,"which are coins made of base .metals., having a square hole in the centre. Thft ends of the string are securely tied, so that the coins once on cannot alter their relative positions one to another. Tha ten coins are marked respectively 2, 8, 9, 0, 7. 1, 5, 4, 6, 3. and are in that order on the string. Can-the reader, without disturbing the arrangement, divide the number:; into three groups, so that onß group-number multiplied by another will produce the number represented by the third group? It may be noted that 3.2 is a group in the same way that 2.8.9 i>, but of course 2.3 is not, nor is 982. CURIOUS SITUATION. Here is a curious situation arising from a sale of articles under peculiar conditions, which were framed most likely for the purposes of a problem and not with regard to-the actual sale of the articles at such differential prices. Seven dealers had between them for sale 560 dozens of these goods, but no one hiid the same quantity as another, and though the goods were of the same kind each had a different grade. Every dealer sold all he had, and the prices charged were the same in each case, notwithstanding the different qualities. Yet strange to say every dealer's takings for the goods were the same in all cases, though every quantity was different, namely, the first man had 20 dozen, the second 40 dozen, the third 60 dozen, and so on, each successive dealer having 20 dozen more than the one before him, the seventh man thus having 140 dozen. The question is that as all the goods were sold at the same rate what price was it ? The reader will, of course, note that a solution of a problem must be based upon the statements expressed in it. and in this case he will not consider the probabilities of such a curious situation happ;ning. MAORI CHIEF'S AGE. Although in this problem unknown quantities are introduced in the form of the letters A and B. the non-mathemat:cal reader is assured that a knowledge of algebra is not necessary to enable the problem' to be solved. Just a few moments thought is all the question calls for. and then by systematic trials, not haphazard, he should quickly arrive at the correct answer. A young student was discussing the age of a Maori chief who had died recently, when his college chum who knew the age. said that ha would put it in the form of a cryptic sum. This is the way he set it. The chief was born in the year A, to the third plus B to the third, which, for the information of the non-academic reader is. the numerical value of A multiplied by itself twice, added to B's value, also multiplied by itself twice. Thus if the respective value of the letters are 2 and 3. the process would he 2 x 2 x 2. plus 3 % x3x 3. Continuing. the student wrote: "Ten years ago the chief's ag« was one year more than seven times B, and his age when he died was A multiplied by B. What was his age if the incident happened this year (1931)-'' LAST WEEK'S SOLUTIONS. An Innovation.—The words are written; backward?, hut six letters, namely, J.K.Q.W.X.Z. have been substituted for 1.D.5.E.T.8. Bartering Scrip.—Jones 200, Smith" 100. Robinson 300. Calls Due on Shares.—W. £l7 10s; X. £l7 10s; Y, £2l; and Z. £lO 10s ; tha total investment being £1330. If Started To-day.—October 27. 1933. Two Deer-Stalkers.—2B miles was travelled altogether by the. two men, whereas the direct route is only 11 miles each way. ANSWERS TO CORRESPONDENTS. " Axiom."—Without the use of fractions there i« no solution of the problem sent, and as these, are not allowed the item is not of any use for this column. j 0 B —The problem " An alphabetical ,um" sent bv J. has been correctly stated, and the equivalent of the- -stter _ A • being the cipher, the l«» » «■ published. The letters have abstract. values which must vary according to their positions when written anthmeW ally The sender of th. problem inada the solution less obvious a word commencing with.- &*,*■