INTELLECT SHARPENERS.

Otago Daily Times, Issue 20708, 4 May 1929, Page 21

INTELLECT SHARPENERS.

By T. L. Briton.

SUM AND DIFFERENCE. It is required to arrange the nine digits in the form of a three-by-three square so tha J perpendicularly, and in the two diagonals, one number subtracted from the sum' of the other two in each of the eight rows stated will have a common difference. This difference may be any number provided it is the same throughout. There are several ways in which the figures, one to nine, can be arranged to produce this result, but if we add the condition that in every direction it must be the middle figure subtracted from the sum of the other two in that particularly column or row, the number of such arrangements is a very small one. Here is one without the latter stipulation:—

Can the reader find any examples under the conditions stated?

' AN EGYPTIAN PUZZLE. A correspondent, "Te Miro," has sent along a geometrical problem which he calls "The Egyptian Puzzle," together with an excellent set of wooden blocks for demonstration purposes made by himself. ; He writes; "I am 75 years of age, and your interesting column gives me much pleasure, as no doubt.it gives to others, so I thought that this,old Egyptian puzzle would interest and'perhaps be .new to most •of your. readers. The problem consists of five wooden square blocks of equal size, each to be cut into two from the centre of • one side to any opposite corner. These 10, pieces are to be arranged in. the form of an exact square, which would not be possible without cutting. 'Very few of my young friends (or o}d ones, for that matter) are able to solve it." ',..■■ This interesting puzzle' involves a useful axiom in mensuration, and is therefore submitted for the reader's consideration and. entertainment, and those not aware of the plan of accomplishing the feat should enjoy the effort of-find-ing it. v Stiff paper or cardboard will answer all purposes. After the r paper has been cut, it will be found that five pieces are equally .shaped triangles, and five trapezoids—that is, quadrilaterals with only two parallel sides. A SQUARE AND A HALF. Whilst on the interesting subject of geometrical problems, here is another one, both useful and instructive. Make a diagram of a four-sided figure. A B C D, with A B and A D at right angles to one another, and equal in length, the bottom side, DC, being P ara " el to A B and exactly twice its length. It will thus be seen that B C .must be equal in length to a diagonal B D, in other words, the figure is a square, attached to which is half of another square of the same dimensions, that is a square and a-half." Now the interesting problem is to find (without bothering with figures),, how this square and a-half can be divided into four figures of equal size and of exactly the same, shape. Do not cut the diagram (which should be drawn as near to scale as possible), but sketch in pencil the wav it should be divided under these stipulations.. There is only one solution. "PRIMUS" AND "SECUNDUS." •fT' , big boys ' Edw ard, Tom, Bruce and Jack each possess a small brother and on a recent Saturday took them to certain sports, each of the young bovs receiving a little money to spend in what manner he pleased. Kenneth spent 2s, Jimmy Is 6d, Max Is, while little Alan expended a whole 6d during the afternoon. Judged by the sums spent by the four tog boys they evidently did not limit themselves to sweetmeats, for it is recorded that although Edward spent T%. the m same am <>unt as his little brother, Tom expended twice as much as ms, Bruce three times as much as his, wfiiie Jacks expenditure was exactly four times that of his young brother. so happened, that there was a sum left over from the pound they had amongst them at first, and as this was pooled and divided in equal shares of one coin each, can the reader find the names of the two brothers who together spent the most, and which two the least, and the sums spent? • It may aid the solver to know that the pound was all in sixpences. A PRINTING PRESS. .While one of*the machines was at work in a certain printing house recently, one the mechani.es was noticed endeavouring to free some cotton waste that had become fastened to a cog on each of two of the wheels that wer* working together. It was not more than a second or so afterwards that he took advantage of the two cogs wtich held the waste, coming together, wlnn in a flash they were removed from both Here ">s a little problem on the point. Let us suppose that there were 32 cogs on one of those wheels and 36 on the other, if the former wheel was making 128 revolutions per second, how often would the same, cogs come together during one. hour's run? ANSWERS TO LAST WEEK'S PROBLEMS. THE WIDTH OF A PATH. The width of the path is on- yard. The following is the method where no measurements are given :—Take a cord the exact length of the plot, hnd by folding it in four, measure a quarter from one corner X marking it A. In the same way mark off a quarter of the short side from the same corner, calling the point B. From A mark a point omi the long side further from the corner, so that A.C. is the same length as X.B. Mark another point at D. on the same line, but closer to the corr.rr, making O.D. equal in length to A.B. Then X.i>. isthe width of the path. This method will apply to any oblong, the path thereby occupying exactly half the area. TWO MEN AND A BOY. The boy would be entitled to 2s only. A GOLF TOURNAMENT. Links. No. 1 O.L. O.R. E.R. L.E. g:f No.'2 R.G. L.F. L.G. F.R. O.E. No. 3- F.E. E.G. P.O. G.O. L.R. AN UNUSUAL BEQUEST. There could be only one distribution—viz., 20 women at 30s .. .. £3O 10 men at 50s £25 Total £55 A TIME LIMIT. Forty-five men under the conditions set 1 out.

ANSWERS TQ CORRESPONDENTS.

“ R.ai‘L.”—Thanks, but it is capable of more than one solution. £*• can, however, be limited to one by adding a condition, and it will appear in this way on May 18. “Lunar.” —A lunar month is 291 days; the period of one complete revolution. J.R.J. ■ Thanks, but has already appeared in this column, and the solution is nineteen, one. and eights'.