Fig. 30.—The paper pointer.
Fig. 30a.—Pointer mounted on cork.
By rubbing the outside of the tumbler with a piece of rag, or even a handkerchief, you can make the pointer turn in whatever direction you desire, as it will swing round to whatever portion of the glass you happen to rub.
Announce that you will make it point to Mr. Jones. If you then rub the glass on the side nearest to that gentleman, the paper needle will swing round and point directly to him.
By rubbing the handkerchief rapidly round and round the glass the needle will be made to revolve with considerable speed, to the great delight of the younger members of the party.
Needle-Threading Extraordinary
Thread a No. 6 needle with a couple of yards of fairly coarse cotton or thread, and draw them through until the two ends are of equal length.
Now pass the point of the needle right through the two strands, as in Fig. 31, and continue pulling the needle as in Fig. 31a until the threads have passed through each other and appear a continuous piece, as in Fig. 31b. This should have been done before showing the trick to the company. As there will be no knot, it is highly improbable that any one will notice a peculiarity in the thread.
Fig. 31.—Needle-threading—first stage.
Fig. 31a.—Thread passing through itself.
Fig. 31b.—Showing thread as a continuous piece.
You then state that, without looking at the needle, you will thread it with as many strands of cotton as it will hold. Proceed in the following way.
Holding the needle with the point upwards beneath the table, out of sight of yourself and the others, catch one of the threads at a point between the eye of the needle and the point where they pass through each other, as in Fig. 32, and pull that steadily downwards.
Fig. 32.—Showing point where thread is pulled steadily downwards.
Fig. 33.—Result of thread passed through eye of needle.
Fig. 33a.—Threaded needle complete.
By doing this the invisible knot is passed through the eye, carrying with it two strands, and by continuing this action the knot is passed several times, until eventually a result similar to that shown in Fig. 33 appears.
Drawing the knot to the bottom of this series of loops, you can then cut off all the ends as well as the knot, and present the threaded needle to your friends as it appears in Fig. 33a.
The Magician’s Bite
Take an ordinary piece of string or thread, and offer to cut it in two if somebody present will guarantee to join it into one piece again without any knot. You may announce at the same time that by wizardry you are able yourself to do this by a simple bite of the teeth.
Fig. 34.—Showing string passed round hands.
Fig. 34a.—Showing ends of string looped together.
The trick is done in this way. Appear to pass the string round the hands twice, as in Fig. 34, whereas by a deft movement, which can be acquired with a little practice, you really loop the two ends round each other, as in Fig. 34a. Holding the point where they cross each other between the finger and thumb (see H, Fig. 35), you request some person to cut the two ends at G, promising to join these ends with your mysterious bite.
Fig. 35.—Showing point where to cut string.
Place the string in both hands into your mouth, and whilst making a mumbling movement, contrive to catch the short doubled piece, G, H, in your teeth and retain it there, whilst extending your hands to the company you show a whole piece of thread, as in Fig. 36. The little piece which you have kept between your teeth can be easily removed without exciting suspicion, and there are few people critical enough to measure the string and find there is a piece missing.
Fig. 36.—Showing whole piece of thread.
A Trick in the Sunshine
This trick can only be done on a sunny day, for a reason which will be very evident to those who try it.
Obtain a clear glass bottle, in the cork of which stick a hooked pin. By means of a piece of thread hang a small weight from this pin within the bottle, as in Fig. 37, and then request some one to cut the cord without drawing the cork.
Fig. 37.—Sun’s rays focused on weighted thread.
All that is necessary to do this is a magnifying glass which is placed between the bottle and the sun at the right distance to focus the rays of the latter upon the cord. In a few seconds the heat of the converging rays will burn through the thread, and the weight will fall to the bottom of the bottle. In the same way you can
Light a Cigarette Without Matches
Concentrate the rays of the sun upon the end of the cigarette, and draw in the ordinary way (if you are old enough to smoke), when the cigarette will rapidly be ignited.
Another String Trick
Stick a penknife into a post or tree, or other strong upright of wood, and pass a piece of string behind the post and above the knife, as in Fig. 38. Bring the end C round the post and pass B over it. Bring C round again and cross it over the knife, and B round the knife over C, as in Fig. 38a. Pass the ends round the post again, always remembering that B must be over C, and then tie the two ends in a knot, as in Fig. 39.
Fig. 38.—Knife and string trick—first stage.
Fig. 38a.—Knife and string trick—second stage.
Fig. 39.—Knife and string trick—third stage.
By removing the knife from the post, you will now find that the whole loop comes away intact, having never really been passed round the post at all.
Try This!
A candle can be lighted without approaching the match to the wick in this way.
Light a candle in the ordinary manner, and take care that the wick is fairly long and burns brightly. Blow it out suddenly, and by applying a lighted match to the smoke at the height of an inch or two, the candle will instantly relight without your having to put the match to the wick.
A Steady Hand
If any of your friends boast of a steady hand, you can easily give their pride a fall by wagering that not one of them can move a glass of water from one table to another without spilling every drop it contains.
Fill a tumbler with water to the very brim. Place a piece of perfectly flat, stout paper on the top of it, as shown in Fig. 40, and the palm of the hand on the top of that. Now turn the glass upside down very quickly and carefully, and place it upon a flat part of the table, having done which slide the piece of paper from beneath it. As the air cannot enter none of the water escapes, but it will be absolutely impossible to move the glass without spilling the water.
Fig. 40.—A water trick.
CHAPTER LXI
“HOW WOULD YOU——?”
Puzzles That Please
History records that the blind poet Homer lost his reason in a vain endeavor to solve a riddle, and from his days until these present times much care and thought have been expended in the invention of puzzles both difficult and simple. It is the object of this chapter to present the reader with a few simple ones.
Two easy and yet fascinating puzzles can be worked with an ordinary checker-board.
1. The Traveling Checker
Place a checker upon a square near the center of the board, as in Fig. 1. In how few moves can you make it traverse every square in the board and return to its starting-point?
Fig. 1.—The traveling checker.
Fig. 2.—Joining the rings.
2. Another Checker Puzzle
Place sixteen men on a checker-board in such a manner that no three men shall be in a line, either horizontally or perpendicularly.
3. Joining the Rings
Nine rings are connected by six straight lines, as shown in Fig. 2. Connect these same nine rings by four straight lines.
4. The Ten Rows
This is a puzzle with nine checkers or counters. Dispose these counters in such a manner that ten rows are formed with three men in each row.
Fig. 3.—The cabalistic sign.
5. The Cabalistic Sign
Fig. 3 shows a piece of paper cut into a famous cabalistic sign. How can you divide it into four pieces which, placed together, shall form a square?
6. The Dangerous Anarchists
Once upon a time there were eight anarchists confined in separate cells connected by the system of passages shown in Fig. 4. The prisoners, each of whom had his own number, occupied cells in the order shown.
One day the governor of the jail decided that his prisoners should be transferred from one cell to another in order that their numbers should run consecutively from left to right. Accordingly he gave orders for this to be done, but at the same time directed his warders that on no account were any two prisoners to meet, either in the passages or cells. As there was only one vacant cell at their disposal, how did the warders work this maneuver successfully?
Fig. 4.—The dangerous anarchists.
You will find the best way to solve this problem is to draw a plan similar to that shown in Fig. 4, and place eight numbered counters in the respective cells.
7. Catching the Donkey
A man once wanted to saddle a donkey, and proceeded, bridle in hand, to the field where Ned was feeding.
Let Fig. 5 represent the field, which the man entered by the gate at 63, whilst the ass was standing in the opposite corner at 2.
Now you can move either the man or the donkey to any number in the straight line, but neither must cross or rest upon a line covered by the other. For instance, if the donkey be at 2, the man can move to 62, 61, 59, 36, or 13; but he cannot go to either 60 or to 5, for then the donkey would gallop up and let fly with his heels. Ned, on the other hand, can go to 6, 28, 51, 3, or 4, but if he were to go to 60 or 5 the man at 63 would catch him at once.
Fig. 5.—Catching the donkey.
Giving the donkey the first move, how soon can you place the man in such a position that the ass is cornered and cannot escape being bridled?
8. Like to Like
Fig. 6.—“Like to like.”
Four black and four white counters are placed alternately in a row of ten divisions, shown in Fig. 6. By moving two at a time, how can you arrange all the blacks and all the whites together in four moves?
9. The Broken Chain
A lady once took to a jeweler a gold chain, broken into five pieces of three links each (Fig. 7). She asked him to repair the chain, agreeing to pay 25 cents for each link that he had to break and weld in order to restore the chain to its original length.
The following day she sent her maid for the chain with 75 cents. If you had been the jeweler, how would you have mended this chain of five pieces by breaking only three links?
Fig. 7.—The broken chain.
10. The Diamond Cross
The same lady wished to have a diamond cross reset, and pleased with the intelligence shown by the jeweler, she decided to give him the work.
Fig. 8.—The diamond cross.
But she was determined to give him no opportunity of cheating her, so she counted the stones from top to bottom (Fig. 8), and found there were nine. She then counted them from the bottom to the extremity of each arm of the cross, and found that they also numbered nine. Having noted these figures, she sent the cross to be reset.
But the jeweler was a crafty man, and knowing how she had reckoned the diamonds, he stole two, and having reset the remainder, he returned the finished piece of work.
When she received her cross, the lady thought it looked rather different, and counted the stones according to her former plan. The numbers were exact! So she paid the jeweler, who went off smiling.
How had he managed the theft?
11. The Quarrelsome Railways
Five competing railway companies decided to place termini in a certain small town. But land was dear; and after much negotiation they were able to secure sites only as shown in Fig. 9.
But none of the companies would grant any of its competitors running powers over its lines, and as the municipal authorities decided that all five lines should enter the city side by side, the engineers found themselves confronted with the following problem:—How is each line to reach its destination, without crossing any of its competitor’s tracks?
How would you extricate them from this dilemma?
Fig. 9.—The quarrelsome railways.
12. Another Railway Problem
This problem is shown in Fig. 10. In the railway A, B, C there are two sidings, A, D and C, E; which meet at F. At this latter place there is only sufficient space to contain one car of the size of G or H, and there is no room for the engine, I. Consequently, if this engine is sent up either of the sidings it must return by the same tracks.
Fig. 10.—The second railway problem.
The point to be discovered is: How can the engine, I, transpose the two cars G and H, by simply using the rails shown in the illustration?
13. The Miter
Study Fig. 11 closely, and think how you can divide a piece of paper thus shaped into four similar parts.
Fig. 11.—The miter.
Solutions
1. The Traveling Checker
You cannot make the checker traverse all the squares in less than sixteen moves, as shown in Fig. 12.
Fig. 12.—Solution to traveling checker.
Fig. 13.—Solution to second checker puzzle.
2. Another Checker Puzzle
The way to place the sixteen pieces so that no three are in a line in any direction, can be seen from Fig. 13.
3. The Rings Joined
The nine rings can be joined by four lines, as shown in Fig. 14.
Fig. 14.—The joined rings.
4. The Ten Rows
The complicated geometrical figure shown in Fig. 15 shows the ten rows formed with nine counters.
5. The Cabalistic Sign
By making the two cuts shown in Fig. 16, the piece of paper will be divided into four parts that will fit together into a square.
Fig. 15.—The ten rows.
Fig. 16.—Solution to cabalistic sign puzzle.
6. The Dangerous Anarchists
The simplest method of rearranging the prisoners was as follows (as there was only one vacant cell at any time the numbers designate which prisoner was moved therein)—1, 2, 3, 1, 2, 6, 5, 3, 1, 2, 6, 5, 3, 1, 2, 4, 8, 7, 1, 2, 4, 8, 7, 4, 5, 6.
7. Catching the Donkey
According to the rules of the game, the donkey moves first, and the following is one of the shortest methods by which the man can catch him. It will doubtless amuse you to find other, and probably quicker ways of cornering Ned.
| Donkey | to | 3 |
| Man | „ | 36 |
| Don. | „ | 21 |
| Man | „ | 30 |
| Don. | „ | 3 |
| Man | „ | 8 |
| Don. | „ | 4 |
| Man | „ | 7 |
| Don. | „ | 5 |
| Man | „ | 12 |
When the man has driven the ass into the corner at 5, of course there is no more chance of escape, and Ned has to submit to the bridle with resignation.
8. Like to Like
Moving two men at a time, the four moves are:—
| 2 | and | 3 | moved to | spaces | 9 | and | 10 |
| 5 | „ | 6 | „ | „ | 2 | „ | 3 |
| 8 | „ | 9 | „ | „ | 5 | „ | 6 |
| 1 | „ | 2 | „ | „ | 8 | „ | 9 |
The counters will then appear as in Fig. 17.
Fig. 17.—Solution to “Like to like” puzzle.
9. The Broken Chain
To repair the chain the jeweler had recourse to a very simple device. Breaking the three links of one of the pieces he used them to join the remaining four pieces, thus restoring it to the original length.
10. The Diamond Cross
The owner of the diamond cross thought she had been very clever in counting the stones as she did, but her cunning overreached itself, for the jeweler had only to remove the diamonds of the extremities of the cross-piece, and shift this latter up one point, as in Fig. 18, to make his theft almost unnoticeable. You will find the diamonds count nine, even though two stones have been removed.
Fig. 18.—Solution to diamond cross puzzle.
Fig. 19.—Solution to the quarrelsome railways puzzle.
Fig. 20.—Solution to miter puzzle.
11. The Quarrelsome Railways
After much surveying and discussion, the railways laid their lines as shown in Fig. 19.
12. The Other Railway Problem
The following is the simplest method by which the engine could transpose the cars G, H.
I pushes G into F, and returns and pushes H up to G. The two cars are then coupled together, drawn down to C and pushed over to A. G is then uncoupled, and I takes H back to F and leaves it there. I then returns to G, pulls it back to E and leaves it there. I then returns to H by way of C, and draws it down to D, thus completing the task.
13. The Miter
A glance at Fig. 20 will show how the miter can be divided into four similar parts.
CHAPTER LXII
SOME OPTICAL ILLUSIONS
When Seeing Eyes are Blind
“But, I tell you, I saw it; surely I can trust my own eyes!”
How often have we heard this uttered as a conclusive proof of some friend’s statement!
And really at first it would seem to be an assertion admitting of no further question, were it not for the fact that we know our eyes are no more infallible than anything else in this world, and are quite as liable to make mistakes as are our memories.
It is true that eyes are good and faithful servants, fit to be trusted in ninety-nine cases out of a hundred, but like all good and faithful servants there is that hundredth case when their judgment goes wandering, and when they leap to rash conclusions, carried away by deceptive appearances.
Strange as it may seem, upon certain occasions, the best eyes are actually blind! If you shut one eye and hold the page with Fig. 1 at arm’s length, you will be able to see both the spots A and B. Now look steadily at A, and you will still see B quite plainly, but if you gradually draw the book nearer to your eye, a certain point will be reached when B becomes invisible, although if you continue to make the book approach your face B will spring into view once more. In other words, at the moment when you could no longer see B your blind spot had been directed towards it, and of course saw nothing.
Fig. 1.—When two are one.
Fig. 2.—Section of the eye.
No doubt you would like to know where this blind spot is, and why our eyes should possess such a thing. Fig. 2 shows the section of an eye which can be explained in very simple terms. The thick black line A is a sheet of nerves which entirely envelops three-quarters of the eye, and meeting in a point at E passes upwards into the brain, where it records what the eye has seen. The light enters between the points C C, the iris, and striking through the lens B throws all objects within the scope of vision upon what is called the retina or screen, D. Now this screen is furnished with millions of little nerves, each one of which records on the large nerve A whatever is thrown upon it, and all these records are gathered together by A and passed up to the brain.
But at the spot E, where these big nerves are collected together, the retina, as you notice, is pointed, and gives no record of what is thrown upon it. So, you see, when any object happens to come into such a position with the eye that its image is cast upon the point E of the retina, we have no record sent to the brain—in other words, we cannot see it.
But the eye is not only blind in one point; it is very apt to be deceived by appearances, and to make all kinds of mistakes in consequence. Take Fig. 3 for instance. Would you not say that B D is shorter than A C? Yet if you measure them you will find they are the same length. Or in Fig. 4, A B is surely longer than C D. They are identical. Or take Fig. 5, A is clearly farther from B than C is from B, and yet A B and B C are of the same length.
Fig. 3.—Is A C longer than B D?
The truth is that your eye is so confused by these different lines that it is wholly unable to form any clear estimate of how great the distances really are. This is shown even more clearly in Fig. 6 (technically known as Zollner’s lines), where you see A B and C D, which have every appearance of being about to meet shortly in the direction of A C. Now if you will measure the distances between B D and A C you will find that the lines are exactly parallel, but the eye has been so deceived by the little cross lines running in different directions, that it seems incredible the two thick lines are not inclined towards one another at quite a considerable angle.
Fig. 4.—Which is longer—A B or C D?
Fig. 5.—The distance from A to B is the same as B to C.
Fig. 6.—Zollner’s lines.
Hills that Don’t Rise
Should it ever happen that you go cycling in France, you will find this deception practiced upon your eyes all day long. The roads in that country are very straight, and are bordered upon either side by tall trees, so that from wherever you stand a long avenue stretches before you to a point where the trees seem to merge into one another, as parallel lines invariably appear to do. But flat as the country may be, you will always find yourself confronted with a gentle incline, as it seems, very slight but none the less perceptible. You brace for a long and steady climb, yet somehow, as you cover the ground, the hill seems always before you and yet there is no noticeable ascent. The reason is simple. There is no ascent. The borders of trees, like the little lines in Fig. 6, deceive the eyes in a similar way until it is almost impossible to believe that the hill is merely an optical illusion, and that the road is flat as the proverbial pancake.
There is another trick the eye is very fond of playing us. A straight line, held on a level with the eye appears very much shorter than it really is. Look at Fig. 7, which appears to represent a number of pins lying with their points towards you. Now lift the book to the level of the eyes, close the right one, and they will appear to be sticking upright in the page.
What a jumble of lines there is in Fig. 8, something like a spider’s web, and one can make nothing out of it. But lift the book up, as in the last example, and close one eye—the letters are plain enough, are they not? You have played a trick on your own eye, and made its habit of shortening lines serve to interpret a message that would otherwise be unintelligible.
Fig. 7.—The standing pins.
Fig. 8.—“Yes or no?”
The Stars don’t Twinkle
Every cloudless night the eyes make a mistake that we can easily discover, but which we are totally unable to remedy.
Of course you have looked up to the sky thousands of times and seen the stars twinkling. Not only that, but if the night is clear you can see they are stellate, or star-shaped, like the starfish which is named after them. You can see both of these things, and yet the strange fact is that neither of them is true!
The stars do not twinkle at all, and they are not stellate. The twinkling is the result of the intervening atmosphere, and not the fault of our eyes; but the second error can be easily brought home to our untrustworthy organs of vision by the following experiment.
Fig. 9.—The illusion of the stars.
Take a piece of tinfoil and prick a small hole with the point of a pin. Now when it is dark put a candle behind the tinfoil in such a way that the light comes through the tiny hole. Hold the tinfoil about ten inches from your face, and the hole will appear irregular. If you bring it nearer, it will lose even the least resemblance to a hole and appear as a star! Of course you know perfectly well that it is round, but your eyes have deceived you once more in the same way that they deceive you every starlight night, and the little hole looks something like Fig. 9—varying slightly with each individual observer. This deception, or to put it charitably, this mistake of the eyes, is given the very high-sounding name of “irregular astigmatism,” but for all that it is an illusion pure and simple.
Like many well-trained servants, the eyes are quite at a loss if anything contrary to the usual routine is presented to them. They know perfectly well the laws of perspective,—how in the ordinary course of nature these laws are never broken by a hairbreadth. They are therefore accustomed to judge in the fraction of an instant the size of an object by its apparent distance away. That this is the result of practice can be easily seen from the fact that very young creatures—human and otherwise—have no idea of the relative distances of objects, and strain to touch a distant gas-light, or, like a young calf, rush headlong into a neighboring wall which their green young fancy deludes them into thinking is really some distance away. But as we grow older we learn many things, and perspective amongst others.
The Dwarf, the Man, and the Giant
Now if we make a drawing such as Fig. 10, which represents three men walking down a passage, our eyes know quite well that if all these men were of the same size, Mr. Jones in front would appear smaller than Mr. Smith behind him. And Mr. Smith in his turn would appear smaller than Brown who closes the procession.
Yet in our illustration Jones appears a veritable giant, towering above Smith and making Brown appear a mere pigmy. If you measure them, you will find they are all three the same size.
The reason of the deception is this. The lines showing the passage disappearing into the far distance immediately suggest to the eye the correct perspective, and, knowing the laws of that perspective, the eye is perfectly convinced that if all three were the same size, Brown in the rear would appear proportionately bigger than Jones. As he does not do so, the eye immediately leaps to the conclusion that he must be very much smaller. It therefore telegraphs to the brain that Brown is a dwarf, following in the tracks of an ordinary man and a giant!