INTELLECT SHARPENERS.

Otago Daily Times, Issue 20906, 21 December 1929, Page 21

INTELLECT SHARPENERS.

By T. L. Briton.

CLEOPATRA’S SQUARE.

As no dqubt the reader at this time of the year will prefer a few problem games as being seasonable, three geometrical puzzles requiring no calculations whatever, and also a couple of problem gomes, are submitted for his mental delectation. The first is the problem known as Cleopatra’s square, somewhat similar to J.C.’s “ Egyptian ” square, which “ D.R.P.” states; both amused and tried the patience of his friends when published some time ago. _ Take a square piece of cardboard or stiff paper of suitable size, say 8:8 inches, with clean-cut edges, and mark the exact centre of each side; then draw a line from each point to an opposite corner so that the two lines from the top and bottom centres will be parallel to one another, and likewise those from the centres of the other two sides, these parallel lines to intersect at right angles. There will thus be a small square shown in the centre, one of whose sides should also be marked in the exact centre, and a line drawn to one if its opposite corners. The cardboard should then be cut along the marked lines with a sharp knife to secure clean edges, and the puzzle is, after well shuffling these ten pieces, to form them into the original square. To do this blindfolded adds to the amusement of the puzzle, and makes it a little more difficult.

THE SHORTEST DISTANCE,

Here is another geometrical problem in which no figures are involved, for It is the method of procedure that has to be found, and if the reader does not know the theory of it, he can determine the question with the aid of a diagram and compasses. A man working at a point A on the south side of a brook which runs oast and west is obliged every evening after work to go to the brook for a supply of water for his hut (H), which is situated some distance e~st of A, and on the same side of the brook. Naturally, the man desires to take the shortest possible route from A to the brook, thence to his hut, and the question he asks is at what point should he reach the brook direct from A in order to ensure this? There is an easy way to determine cases of the kind, the mathematical method of finding it being well rth knowing, and it is sc simple that if a diagram be made from the description gi. en the reader no doubt will be able to discover it quite easily. A simple calculation afterwards will " prove ’’ the correctness or otherwise of any solution arrived at, or compasses would do equally as well, , 1

WITH THE DICE,

A very interesting puzzle game with three dice is one involving a little mental arithmetic, and for a while it is quite likely, to perplex anyone not acquainted with the method. As everyone knows, dice are cubes of a size suitable for handling, whose six sides are numbered respectively 1,2, 3,4, 5, 6. Let one of the party throw the three dice on the table, unseen by the person .'emonstrating the puzzle, who will ask the thrower to multiply the number of spots uppermost on the first die by two and to add five, then to multiply the result by five and to add the spots uppermost on the second die, and finally to multiply that result by ten adding the number of spots uppermost on the third die. When the thrower gives this result, the demonstrator is able at once to, tell him how the dice were thrown. For example, if the result of the calculation is 484, the demonstrator would be able at once to say that the dice thrown, were 2,3, and 4. Examine this with the three dice in demonstration, and try to discover how it is done, for it is an interesting puzzle.

ARTIFICE AND SCIENCE.

Some mathematical knowledge is required to enable a person to draw an oval scientifically, but there is a method by artifice which enables this to be done by any person unacquainted with practical geometry with one turn of the ordinary compasses. The method was explained in this column a good while back, and it is recollected that a correspondent wrot> nt the time that the'method was not practicable, as. she had made repented unsuccessful attempts to achieve the desired result. The writer of these notes, however, has demonstrated its practicability frequently, and since publication has seen others perform the trick (for it is a trick, though useful to know), without any difficulty whatever, after the method was once explained.

ONE WITH THE CARDS,

And here is one with the cards which should give the reader some intellectual amusement, tor it Involves a little arithmetic, Take the nine cards one to nine, and arrange them in the form of a triangle with four on each aide (three of them counting twice), so that the spots will add up the same on the three sides. For example, place the .sevfen at the apex soI’that 1 ’that the sides reading downwards will be four, three, nine, and two. six, eight 'respectively, the base from left to right being nine, five, one, eight Each side adds up 23, which is the highest number possible, all adding the same. Now, the interesting puzzle for the reader is to arrange these nine cards in the form of a similar triangle so that all sides, of four cards each, total the smallest number possible.

LAST WEEK’S SOLUTIONS. IN WHAT YEARS? Jenkins and his second spouse were born in 1856 and 1892 respectively, the wives being 18 years old on their wed„ding days. COLENSO’S CURIOUS CONUNDRUM. Born 1860. CROWDED TRAINS. As £54 lie 8d represented the value of the tickets held by those left behind, there must have been 122 first-class passengers and 366 who travelled second. TIME IS MONEY. The cost would be £6OOO if the gang comprised half of each of the two classes of labourers. WHILST SHARPENING THE PENCIL. 1. Hi seconds. 2. Six days. ANSWERS TO CORRESPONDENTS. “ Query.”—The same mathematical signs are used to denote minutes and seconds in circular measurement as those indicating feet and inches. (2) The other sign you mention means the difference wetween two unknown quantities, leaving it doubtful which is the greater. “ China.”—There is no proper system of weights and measures established by Government in China. The chief treaty weights are:—“Tael,” IJoz; “catty,” IJlb; and the “picul,” 133 Jib. (2) The “tael” is not a

currency. C. V. R.—lt appeared on November 2. “ Santa Claus.”—Thanks for greetings, and comments appreciated. “English.”—(l) “Typist” is correct, not “ typiste.” The latter, however clearly suggests the “ female of the species,” and as such will possibly bo found in future lexicons. (2) “ Stockist ” is a coined word, and when used by a shopkeeper has an obvious meaning. A. Cooper.—There is only one solution, as the problem read “ largest number.”