Part 6 (1/2)
156--THE DISSECTED TRIANGLE
A good puzzle is that which the gentle to his friends He has sile--that is, a triangle with all its three sides of the sath He proposes that it shall be cut into five pieces in such a way that they will fit together and for all the material in each case Can you discover how the cuts should be made?
Remember that when you have made your five pieces, you ether to forles or to forles--all equilateral
157--THE TABLE-TOP AND STOOLS
I have frequently had occasion to show that the published answers to a great many of the oldest and most widely known puzzles are either quite incorrect or capable of improvement I propose to consider the old poser of the table-top and stools that most of my readers have probably seen in some form or another in books compiled for the recreation of childhood
The story is told that an econoenious schoolmaster once wished to convert a circular table-top, for which he had no use, into seats for two oval stools, each with a hand-hole in the centre He instructed the carpenter to ht pieces together in the enuity of his perforeometry class as a little study in dissection But the remainder of the story has never been published, because, so it is said, it was a characteristic of the principals of acadeet inal boy who had most reason to be interested in the ested , and that a sh the the cuts that would get over this objection For his impertinence he received such severe chastiseer the hand-hole in the stools the ht they be
[Illustration]
Noas the method the boy proposed?
Can you sho the circular table-top ether and form two oval seats for stools (each of exactly the sa similar hand-holes of smaller dimensions than in the case shown above? Of course, all the wood must be used
158--THE GREAT MONAD
[Illustration]
Here is a symbol of tremendous antiquity which is worthy of notice It is borne on the Korean ensign and n by the Northern Pacific Railroad Coh probably few are aware that it is the Great Monad, as shown in the sketch below This sign is to the Chinan of Deity and eternity, while the two parts into which the circle is divided are called the Yin and the Yan--the male and female forces of nature A writer on the subject o is reported to have said in reference to it: ”The illireat extreme produces the two principles The two principles produce the four quarters, and froht diagrams of Feuh-hi” I hope readers will not ask htest idea what it es the sys for the esoteric student
I will introduce the Monad in its elereat syreater area, the inner circle containing the Yin and the Yan, or the outer ring?
(II) Divide the Yin and the Yan into four pieces of the same size and shape by one cut
(III) Divide the Yin and the Yan into four pieces of the saht cut
159--THE SQUARE OF VENEER
The following represents a piece of wood in s on the surface it is divided into twenty-five square inches I want to discover a way of cutting this piece of wood into the fewest possible pieces that will fit together and form two perfect squares of different sizes and of known dimensions But, unfortunately, at every one of the sixteen intersections of the cross lines a small nail has been driven in at some time or other, and my fret-saill be injured if it comes in contact with any of these I have therefore to find athrough any of those sixteen points How is it to be done? Reiven
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160--THE TWO HORSESHOES
[Illustration]
Why horseshoes should be considered ”lucky” is one of those things which no man can understand It is a very old superstition, and John Aubrey (1626-1700) says, ”Most houses at the West End of London have a horseshoe on the threshold” In Monmouth Street there were seventeen in 1813 and seven so late as 1855 Even Lord Nelson had one nailed to the mast of the shi+p Victory To-day we find it ood luck” to see that they are securely nailed on the feet of the horse we are about to drive
Nevertheless, so far as the horseshoe, like the Swastika and other emblems that I have had occasion at times to deal with, has served to syoodwill towards men, we may well treat it with a certain amount of respectful interest May there not, moreover, be some esoteric or lost mathematical mystery concealed in the for into this matter, and I wish to draw my readers' attention to the very remarkable fact that the pair of horseshoes shown inand beautiful manner to the circle, which is the symbol of eternity I present this fact in the form of a simple problem, so that it es and ages My readers will, I know, be pleased when they find the key to the mystery
Cut out the two horseshoes carefully round the outline and then cut theether and form a perfect circle Each shoe must be cut into two pieces and all the part of the horse's hoof contained within the outline is to be used and regarded as part of the area
161--THE BETSY ROSS PUZZLE
A correspondent asked me to supply him with the solution to an old puzzle that is attributed to a certain Betsy Ross, of Philadelphia, who showed it to George Washi+ngton It consists in so folding a piece of paper that with one clip of the scissors a five-pointed star of Freedoin is a true one or not I cannot say, but I have a print of the old house in Philadelphia where the lady is said to have lived, and I believe it still stands there But my readers will doubtless be interested in the little poser
Take a circular piece of paper and so fold it that with one cut of the scissors you can produce a perfect five-pointed star
162--THE CARDBOARD CHAIN
[Illustration]
Can you cut this chain out of a piece of cardboard without any join whatever? Every link is solid; without its having been split and afterwards joined at any place It is an interesting old puzzle that I learnt as a child, but I have no knowledge as to its inventor
163--THE PAPER BOX
It h it is not strictly a puzzle, an ingeniousa paper box
Take a square of stout paper and by successive foldings make all the creases indicated by the dotted lines in the illustration Then cut away the eight little triangular pieces that are shaded, and cut through the paper along the dark lines The second illustration shows the box half folded up, and the reader will have no difficulty in effecting its coht cut out the circular piece indicated in the diagram, for a purpose I will now explain
This box will be found to serve excellently for the production of vortex rings These rings, which were discussed by Von Hel, and the box (with the hole cut out) will produce the it gently through the hole Now, if you hold it horizontally, and softly tap the side that is opposite to the hole, an is can be produced from one mouthful of smoke It is best that there should be no currents of air in the roos are formed in the air when no smoke is used The ss, if properly directed on its course, will travel across the room and put out the fla if you can e to do it without the ss may be blown froreater perfection, and no skill whatever is required Lord Kelvin propounded the theory that s in a fluid that fills all space, and by a development of the hypothesis he was able to explain chemical combination
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[Illustration]
164--THE POTATO PUZZLE
Take a circular slice of potato, place it on the table, and see into how large a number of pieces you can divide it with six cuts of a knife Of course you must not readjust the pieces or pile thereatest number of pieces you can make?
[Illustration: -------- / 1/ / 2 / 3 / / / / / 4 / 5/ 6 / | / / / | 7/ 8/ 9/10 / / / / / /11/12/13/ / / / /14/15/ / / /16/ ----- ]
The illustration sho to make sixteen pieces This can, of course, be easily beaten
165--THE SEVEN PIGS
[Illustration]
+------------------------------+ | | | P | | | | P | | P | | P | | P | | P | | P | | | +------------------------------+ Here is a little puzzle that was put to one of the sons of Erin the other day and perplexed him unduly, for it is really quite easy It will be seen from the illustration that he was shown a sketch of a square pen containing seven pigs He was asked hoould intersect the pen with three straight fences so as to enclose every pig in a separate sty In other words, all you have to do is to take your pencil and, with three straight strokes across the square, enclose each pig separately Nothing could be simpler
[Illustration]
The Irishs would not keep still while he was putting up the fences He said that they would all flock together, or one obstinate beast would go into a corner and flock all by himself It was pointed out to his were stationary He answered that Irish pigs are not stationery--they are pork Being persuaded to h a pig When it was explained that this is not allowed, he protested that a pig was no use until you cut its throat ”Begorra, if it's bacon ye ithout cutting your pig, it will be all ga that the miserable pun was intentional However, he failed to solve the puzzle Can you do it?
166--THE LANDOWNER'S FENCES
The landowner in the illustration is consulting with his bailiff over a rather puzzling little question He has a large plan of one of his fields, in which there are eleven trees Now, he wants to divide the field into just eleven enclosures by ht fences, so that every enclosure shall contain one tree as a shelter for his cattle How is he to do it with as few fences as possible? Take your pencil and draw straight lines across the field until you have marked off the eleven enclosures (and no more), and then see how many fences you require Of course the fences may cross one another
167--THE WIZARD'S CATS
[Illustration]
A wizard placed ten cats inside a ic circle as shown in our illustration, and hypnotized the his pleasure He then proposed to draw three circles inside the large one, so that no cat could approach another cat without crossing a ic circle Try to draw the three circles so that every cat has its own enclosure and cannot reach another cat without crossing a line
168--THE CHRISTMAS PUDDING