"NUTS!"

Evening Post, Volume CVII, Issue 102, 4 May 1929, Page 15

"NUTS!"

| INTELLECT SHARPEIERS I All rights tmerrti.

(By T. I*. Britoa.)

Beaders with * llttla Ingenuity will find ia this column aa attendant store of entertainment and aunaement, and the solving of tha problems riumld proride excaUaat mental exhilaration. Wail* torn* of the "nuts" may appear harder than othera, It will b« found that none will requiw a aledo-AamiMc to crack them.

SUM AND DHTEBENCE. It ia required to arrange the niae digits in the form of a three by three square, so that horizontally, perpendicularly, and in the two diagonals one number subtracted from the sum of the other two in each of the eight rows stated will havo 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 particular column or row, the number of such arrangements is a very small one. Here is one without the latter stipulation: —

But can the reader find any examples under the conditions stated? AN EGYPTIAN PUZZLE. A correspondent, "Te Miro," has sent along a geometrical problem which ho calls "The Egyptian Puzzle," together with an excellent set of wooden blocks for demonstration purposes made by himself. Ho writes:—"l am 75; years of age, and your interesting column gives me much ploasuro, 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 leaders. The problem consists of five wooden square blocks of equal 6izc, j each to be cut into two from tho centre of one side to • any opposite corner. These ten 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 old ouos for that matter) are able to solve it." This interesting puzzle involves a useful axiom in mensuration, and ig therofore submitted for the reader's consideration and entortainment, and those not aware of the plan of accomplishing the feat should enjoy the effort of finding it. Stiff paper or cardboard will answer all purposes, and after cutting 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. | AVbilst on the interesting subject of geometrical problems, hero is another one, both useful and instructive. Make a diagram of a four-sided figure A.8.C.D., with A.E. and A.D. at rightangles to one another and equal in length, the bottom side D.C. being parallel to A.B. and exactly twice its length. It will thus be seen that B.C. must be equal in length to a diagonal 8.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. 51 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 way it should be divided undor these stipulations. There is only one solution. "PRIMUS" AND "SECUNDUS." Four big boys, Edward, Tom, Bruce, and Jack, each possess a small brother, and on a recent Saturday took them to the "sports," each of the young boys receiving a little money to spend in what manner he pleased. Kenneth spent two shillings, Jimmy eighteenpenee, Max one shilling, while little Alan expended a whole sixpenco during the afternoon. Judging by the sums spent by the four big boys' they evidently did not limit themselves to sweetmeats, for it is recorded that although Edward spent only the same amount as his little brother, Tom expended twice as much as his, Bruce three times as much as his, while Jack's expenditure was exactly four times that of his young brother. Now it so happoned that thore was a sum loft over from the pound they had amongst thorn at first, and as this was pooledand 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 watching one of the machines at work in a.certain printing houso recently, one of the mechanicians was noticed endeavouring to free some cotton waste that had become fastened to a cog on each of two of the wheels that were working together. It was not more than a second or bo afterwards that he took advantage of the two cogs which held the waste coming together, when in a flash they wcro removed from both. Here is a little problem on the point. Let us suppose that there were thirty-two cogs on one of those wheels and thirty-six on the other. If the former wheel was .making one hundred and twenty-eight revolutions per second, how often would tho 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 one yard. Tho following is the method whore no measurements are givon:—Take a cord the exact length of the plot, and by folding it in four measure a quarter from ono 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 C on the long side further from the corner, so that A.C. is the same length as KB. Mark another point at D. on the same line, but closer to the corner, making C.D. equal in length to A3. Then X.D. is tho wU2*\ 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. No. 1 Links O.L. O.K. E.R. L.E. G.V. No. 2 Links K.G. L.F. L.G. F.R, O.E. No. 3 Links F.E. E.G. F.O. G.O. L.R, An Unusual Bequest.—There could be only one distribution, viz.: 20 women at 30s, £30; 10 men at 50s, £25; total, £55. A Time Limit. —Forty-five men under the conditions set out. ANSWERS TO CO-RESPONDENTS E. ML.—Thanks, but it is capable of more than one solution. It can, however, be limited to one by adding a condition, and it will appear iv this way 18th Miv. 1929. "Lunar."— a. lunar month is 29 i days; the period of one complete revolution. J.R.J.—Already appeared in this column, and the solution is nineteen, eighty and one.