HOW?
OR,
SPARE HOURS MADE PROFITABLE.
THE WINDMILL PUPPET.
This amusing little puppet is very easily constructed, and, like several other mechanical toys in this book, furnishes much entertainment for the little folks. Even the baby will sit in her high chair, half-hours together, watching the little man turning his crank, while she claps her tiny hands and crows at so delightful an exhibition of untiring energy.
Cut from cardboard a disc like Fig. 2, which shall measure about six inches across; then by means of a ruler draw the lines a b c d; half-way between these points make four others, corresponding to e f g h; and lastly, between all these, still another set of lines. Make the circle, m, one-and-a-half inches in diameter, and with a pair of sharp scissors cut through all these lines, to the edge of the smaller ring. Bend one edge of each of these triangular pieces slightly upward, as indicated by the shading, and the opposite edge downward; also bend a piece of wire a foot long, so as to form the crank indicated in the illustration.
Next make a frame-work for the figure to rest upon: this should consist of a three-cornered piece of wood, six inches long for the bottom, a stick six or seven inches long for the upright, and lastly, the support for the upper part of the wire, with a small hole in one end for the latter to pass through. Fasten these pieces together with small brad-nails, and secure the upright to the bottom piece by a screw or nail passing up from below. The wire, having the crank already bent in the proper place, may now be passed up through the hole, and the other end sunk down into another, bored a short distance into the bottom board, directly below the upper one. Then the wire may be fastened to the windmill, by passing it through a little one side, then back again through on the other side of the center; twisting the end once or twice about the main stem beneath the windmill; it now turns with the windmill, and it is needless to say that the friction in the holes should be as slight as possible.
The figure is to be cut from a piece of cardboard and is made in five pieces. The lower half, which comprises the box, legs, and body up to the dotted line, is in one piece; the head and body to the lower edge of the belt, consists of two pieces, cut precisely alike, and lapping on either side of the lower part of the body over the dotted line, to give strength to the image. A pin passed through the belt, and bent down on the other side, will hold it in place, and allow sufficient play to the figure. There are two arms, cut from the same pattern, and pivoted at the shoulders with another pin. The hands are finally brought together, with the crank between them, and lightly secured on either side with two or three stitches.
To impart life to this creation, it is placed over a furnace register through which the hot air is briskly rising. If the machine works easily, the current of air above a stove may suffice.
THE FLYING WHIRLIGIG.
This amusing toy consists of an empty spool with two pins driven into its head, as seen in the figure. With a pair of pliers break off the heads of the pins before driving them in position, then take a piece of soft wood and make a spindle, like that represented in the figure at A, and drive another headless pin into the small end. Lastly, cut from a piece of cardboard a figure like the one marked B, making three holes, a a a, with the point of a darning-needle, corresponding to the two pins in the spool and the one in the spindle.
Bend the edges marked x and y in opposite directions.
Now place the spool on the spindle and wind a piece of twine around the spool; then place the piece of pasteboard upon the top, letting the pins pass up through the row of holes in its center.
Holding the machine upright in the left hand, with a quick movement of the right, jerk the string from the spool, and the cardboard will fly through the air with a very graceful motion.
If stripes of color are added to the ends, as seen in the cut, a much prettier effect is produced while the whirligig is in operation. These stripes can be painted in red, white, and blue water colors, or may be formed by pasting on narrow strips of bright-colored paper.
If the first trial does not succeed, wind the string in the other direction, or put on the “card flyer,” with the other side next the spool. The same causes which make it soar away in the one case will hold it yet more firmly to the spool in the other.
HOW TO MAKE A BOOK.
Do any of my boy readers know how to make a book? Not the fine volumes turned out by the thousand in our great publishing houses, but the little individual books made by boys and girls, and needing for their construction only an old used-up ledger, a small tin pan of paste, and scraps cut from newspapers or books. These bits may consist simply of poems, or they may be “a little of all sorts.”
I recently saw a very nice book of this kind made by a boy of twelve, which was composed entirely of humorous pictures and jokes, culled from several illustrated and daily papers, one or two almanacs, and various other chance publications, which he had collected during the year. Whenever he found any bright or witty thing, he would carefully preserve the clipping by putting it in a large paper box he kept in a convenient place for that purpose.
He reserved the pasting for rainy days and winter evenings, and as he took much pains with the arrangement and neat appearance of his book, this operation was necessarily slow, and formed a pleasant occupation for many hours which would otherwise have been wasted.
In making such a book, do not try to complete it in a week or even a month, but let it, like my boy friend’s, furnish amusement for a year.
Get your father and mother interested, and ask them to save any scraps they may see, and think appropriate for the purpose.
A handsomely bound scrap-book, specially designed for this use, would certainly be the most desirable thing to have; but if such a book cannot be obtained, an old ledger does very nicely in its place, and if, after it is completed, you cover it carefully with a piece of smooth brown paper and print its title neatly on the back, it will look very well on any table where you may wish to keep it.
If the latter is used, cut from it every other two leaves, reserving the third, through the book. Next be careful to trim all your clippings neatly, leaving no extra paper beyond the edges. Fit the different slips nicely on the pages, filling the little spaces left from the longer articles with any little jokes or bits of poetry you may have. Frequently a whole piece of newspaper poetry is hardly worth preserving, but some one of its stanzas may be very pretty and just the thing to fill up a place you may have left.
It is well to collect all these little things you can find, for they always come in nicely when pasting, and your book looks much better when finished if the original surface is entirely covered.
THE SNAKE.
Cut from a piece of Bristol board, or stiff paper, a circle measuring four inches in diameter; then with a pencil mark it like Fig. A. With your paints and pencil make its head as nearly like a snake’s as possible; and mark the body with stripes or checks, as your fancy may dictate. Cut through the deep black line, put a pin through the dot on the tail, and drive it into a slender stick of wood, which must be held or caught over the stove or register. The rising current of heated air causes the snake to revolve and apparently writhe, in a very natural manner. This little toy, so simple in its construction, affords an endless amount of entertainment to the little folks of the family, and is well worth the trouble and time you may spend in making it.
The hot air from a lamp or gas jet will also impart activity to this mimic reptile.
THE DIVIDED SQUARE PUZZLE.
Take a square of paper or cardboard, and cut it into four pieces, as shown in the engraving. Now try to put them back in the form of a square. This seemingly simple puzzle, has kept our young people busy a whole evening, and was only accomplished at last by marking each piece before it was cut apart.
EXPERIMENT WITH TWO PIECES OF GLASS.
Procure two pieces of glass about six inches square, join any two of their sides, and separate the opposite sides with a piece of wax, so that their surfaces may be at a slight angle; immerse this apparatus about an inch in a basin of water, and the water will rise between the plates and form a beautiful geometrical figure called a hyperbola.
THE GRIMACING FACE.
Take a card one-and-one-half inches wide, and fold around it a piece of unruled note paper, so that the card can easily slide up and down; then paste this case on the under side. Now cut three holes in the paper for the eyes and mouth, as seen in A; place the strip of card within this and mark the points for the eyes and root of tongue; then slipping it out once more, the eyes can be carefully finished, and the tongue cut to fit in the mouth, and to extend some distance down on the chin, see Fig. B. Then by putting the two pieces together, pulling the tongue in its place through the opening, very amusing expressions can be produced, by simply moving the pasteboard up and down in the paper. Fig. C represents the two parts put together.
A GOOD BALL.
Take a round, well shaped orange; cut it evenly into quarters, numbering them at one end to aid in putting the parts together again. Next cut out of kid four pieces exactly like the four pieces of orange peel; then, with strong linen thread, sew over and over three seams, thus joining the four pieces, but leaving one seam open. In putting together be careful to place 1 next to 2, and so on, just as they were in the orange. Ravel out an old yarn stocking, or cut into narrow strips an old cashmere one, and after making a little round ball of any soft woolen material, commence winding it evenly with the raveled yarn, trying occasionally if it is near the size of the kid covering. When nearly large enough wind it in such a way that it shall just fit the cavity, and then carefully sew up the remaining side.
Great care should be exercised in forming the inner ball, and in cutting the kid. The wrists of old kid gloves make capital coverings. An old rubber overshoe cut in very fine strips and wound carefully, forms a nice center, but it is better to use the soft wool yarn next the cover, as it is more pliable and makes a better shaped ball.
Prepare this ball during your leisure moments in the long winter evenings; and it will then be ready for the first game, when the bright spring sunshine reminds you of summer sports once more.
AMUSING EXPERIMENT WITH TOOTH-PICKS.
Take five tooth-picks, weave them together, as seen in the illustration, which perhaps is easiest done by holding the three diverging ones between the thumb and forefinger of the left hand at the point a, and insert the other two successively, first b, then c. Now lay the figure upon any flat surface, letting the end c extend a short distance beyond the edge. If you touch a lighted match to c, in a moment each stick will leap into the air as if suddenly endowed with life and animation, quite unusual in such inert objects.
HOW TO CUT TOPS FROM GLASS BOTTLES.
A glass bottle when freed from its top can be utilized in many ways, and most boys will be glad to know how to get rid of this troublesome portion without smashing the whole thing into fragments.
A red-hot poker with a pointed end is the instrument used. First make a mark with a file to begin the cut; then apply the hot iron, and a crack will start, which will follow the iron wherever it is carried. This is, on the whole, simple, and better than the use of strings wet with turpentine, etc.
A BOY’S BAROMETER.
Take a common vial, or small bottle, cut off the rim by using the hot poker as directed above. Let the vial now be nearly filled with common rain water, and applying the finger to its mouth, turn it quickly upside down: on removing the finger it will be found that only a few drops will escape. Without a cork or stopper of any kind, the water will be retained within the bottle by the pressure of the external air, the weight of the air without the vial being so much greater than the small quantity within it. Now let a bit of tape be tied round the middle of the bottle, to which the two ends of a string may be attached, so as to form a loop to hang on a nail; let it be thus suspended in a perpendicular manner, with the mouth downward: and this is the barometer.
When the weather is fair, or inclined to be so, the water will be level at its lower surface, or perhaps concave, like an individual butter plate turned upside down; but when disposed to be stormy, a drop will appear at the mouth, which will enlarge till it falls, and then another drop, so long as the humidity of the atmosphere continues.
AN INFALLIBLE BAROMETER.
With a few cents any boy can buy the chemicals required for this barometer, and obtain an instrument much more reliable than many of the cheaper grades for sale in the stores. Put two drams of pure nitrate of potash, and half a dram of chloride of ammonium reduced to a powder, into two ounces of pure alcohol, and place this mixture in a clear glass bottle, covering the top with a piece of rubber or thin kid pierced with small holes.
If the weather is to be fine, the solid matters remain at the bottom of the bottle, and the alcohol is as transparent as usual. If rain is to fall in a short time, some of the solid particles rise and fall in the alcohol, which becomes somewhat thick and troubled. When a storm, tempest, or even a squall is about to come on, all the solid matter rises from the bottom of the bottle and forms a crust on the surface of the alcohol which appears to be in a state of fermentation. These appearances take place twenty-four hours before the tempest ensues, and the point of the horizon from which it is to blow is indicated by the particles gathering most on the side of the tube opposite to that part whence the wind is to come. The longer the diameter of the bottle the better for this kind of barometer.
THE BALANCING DOLL.
From a piece of soft wood whittle out a head and body like that in the illustration, making slits on either side for the insertion of the wings. These oar-shaped appendages are generally made from a shingle, and are affixed to the body by pressing them firmly into the slits. The whole thing can be painted to suit the fancy; water colors spread on rather thickly answer quite as well for small objects of this class, if protected by a good coating of varnish, made by dissolving a few cents’ worth of white shellac in a small quantity of alcohol. It is important that the oars are of the same weight and placed at equal angles with the body for this plaything to be successful.
THE BOOMERANG.
The boomerang is a weapon which has long been known as peculiar to the Australian savages, who are wonderfully skilled in its use.
It consists of an irregular shaped piece of hard wood, so constructed that by its aid, the unsuspecting game can be killed at an angle widely diverging from the line of direction in which it was thrown. Instances have been cited in which the boomerang, in the hands of these untutored savages, has accomplished wonderful feats. One of the favorite ways of throwing consists in sending the weapon in such a manner that it shall skim along just above the ground for about a hundred feet, then, rising in the air, double back upon its course, and hit a mark only a few feet in front of the thrower. Of course we do not expect to equal the savages in its use, when recent investigations show that it has taken the experience of generations upon generations of men and hundreds of years, to bring it to its present degree of excellence; but every boy may derive much fun from practicing with the little cardboard boomerang cut of stiff pasteboard in either of the forms given in the preceding page. To throw this, place it upon a book, one end extending beyond the edge; then, with a ruler or small stick, strike it forcibly upon the edge, and it will fly through the air and back again, in an amusing, lively manner, quite unlike any other missile in a boy’s collection. It may be sent on its way by simply snapping it with the forefinger of the right hand while it is held on the book in your left. If you should try making one of wood to use out-of-doors, try it in the middle of a large open lot, for there is no telling what mischief it might do if it only had the chance.
THE MAGIC TELESCOPE.
The following, although requiring considerable skill in joining, can readily be made by any boy of fifteen, if he is at all skillful in the use of carpenter’s tools, and has a fair endowment of those two excellent qualities, patience and perseverance, so absolutely indispensable to success in almost any undertaking.
This telescope consists of a series of square wooden tubes, with an inside diameter of about five inches, so carefully joined together that no ray of light can find its way in through the crevices. The oblique lines are pieces of looking-glass, with their faces turned toward each other. Now, by placing the eye at E, of course it would seem that anything at H could be seen directly through the tubes A B, while if a book or other opaque object be interposed, as shown in Fig. 2, it would seem equally a matter of course that the view would be obstructed; this, however, is not the case, as the mirrors reflect the object through the tube and it appears as plainly as when the book is removed.
To those unfamiliar with its construction this magic telescope, by which you apparently see through a solid substance, is an unfailing source of wonder.
The object at H should be quite brilliantly lighted, as some of the rays are absorbed in the passage of the reflection through the tube; especial care should also be taken to place the mirrors at a slant, exactly midway between the horizontal and the upright, or, to speak more scientifically, at an angle of 45 degrees to the line of the tubes.
The tubes A and B should not be so far apart at the place where the book is inserted as to permit the backs of the mirrors to be easily seen.
TO CRYSTALLIZE GRASSES, SEED-VESSELS, Etc.
Take a large-sized piece of alum, and pour over it a pint of boiling water, letting it stand until the water has taken up or dissolved all the alum it will. If at the end of a few hours any alum remains undissolved, you may be sure the water contains all the alum it can hold in a liquid state, and the solution is called a “saturated solution of alum.”
During the summer, while the grasses are in their most perfect state, select such as you think will look well crystallized, and put them into a vase or wide-mouthed bottle to dry, being careful to spread them well apart, so that they may retain their perfect shape in drying. If the season of grasses should pass before you have a chance to collect them, the season of weeds is always at hand. Any boy, in his wanderings over marsh or mountain, through woods or our quiet village street, during even the coldest winter months, could not fail to see some beautiful sprays of seed-pods crowning many of our most common weeds, which if crystallized, would make a very pretty and acceptable present to mother for the corner bracket, or the shelf which seemed just a little bare before. Having secured your grasses or weeds, both together if you like, and having your saturated solution of alum at hand, lay as many tops of the grasses in a flat dish as will fill it without crowding, then pour the liquid over them, being careful that the parts you wish crystallized are under the surface. Let them lie in this position until well coated with the alum. When finished remove them and put in others. Continue in this manner until all are treated. If only a few crystals are desired they may be obtained by dipping the heads one at a time in the solution and slightly shaking them after each immersion. When all have been dipped, commence with the first and repeat the process. Do this until the crystals formed are as large as you wish them to be.
METHOD OF COLORING ALUM CRYSTALS.
In making these crystals the coloring should be added to the solution of alum in proportion to the shade which it is desired to produce. Coke, with a piece of lead attached to it in order to make it sink in the solution, is a good substance for a nucleus, if a cluster of crystals are to be formed. Any form, if wound around with knitting cotton, can be used, or the grasses above described can be dipped in these colored solutions, and very pretty results obtained.
Yellow: muriate of iron. Blue: solution of indigo in sulphuric acid. Pale blue: equal parts of alum and blue vitriol. Crimson: infusion of madder and cochineal. Black: Japan ink thickened with gum. Green: equal parts of alum and blue vitriol, with a few drops of sulphate of iron. Milk white: a crystal of alum held over a glass containing ammonia will become a milky white color upon its surface.
[Note.—To make an infusion of a substance you simply pour boiling water over it. The madder and cochineal are in the dry form, and only a little water should be used, as too much will make the color less brilliant.]
ANIMATED FIRE.
When small pieces of camphor are placed in a basin of pure water, a very peculiar motion commences; some of the pieces turn as if on an axis, others go steadily round the vessel, some seem to be pursuing others, and thus they continue forming a very curious and pleasing appearance; but if a single drop of sulphuric acid be put into the water, the motion of the camphor instantly stops. If a piece of camphor be lighted, and then carefully placed on the water, it burns with a bright flame, moving about with great rapidity, as if in search of something, but is instantly stopped by a drop of sulphuric acid.
A PRETTY ORNAMENT FOR A BOY TO MAKE.
Dissolve in seven different tumblers containing warm water, half ounces of sulphates of iron, copper, zinc, soda, alumina, magnesia, and potash. Pour them all, when completely dissolved, into a large flat dish, and stir the whole with a glass rod or bit of broken glass for a while. Place the dish in a warm place where it will be free from dust and will not be shaken. After due evaporation has taken place, the whole will begin to shoot out into crystals. These will be of various colors and forms, some little ones being gathered together in small groups, and other larger ones scattered throughout the whole fluid. By a little careful study you will soon be able to distinguish each crystal separately, from its peculiar form and color, thus learning an interesting lesson in chemistry, while making a beautiful ornament for your room. Be sure and preserve it carefully from the dust.
HOW TO MAKE A BLOWPIPE.
Procure two common clay pipes; break off the stem of one about three inches from the little end. Take a cork that exactly fits into the bowl of the other pipe, cut a hole through it large enough to insert the mouth-piece already broken off, and draw this through the opening till its larger end is even with the surface of the cork. Insert the cork in the bowl, and fill the end of the stem which touches the flame with a tiny ball of clay or chalk. Through this clay make a hole with a needle, and a blowpipe is the result, which answers very well for any experiment a boy may be likely to try.
HOW TO BLOW GLASS.
Although it is impossible to give any detailed account of glass blowing which would be practicable for small boys, yet a child can amuse himself for hours, by simply melting bits of glass and joining them together; or by melting small glass tubes and drawing them out to mere threads; or again, blowing them up into tiny balloons until their surface is as thin as a soap bubble and almost as fragile. These little tubes are smaller than the end of a pipe-stem, about four inches long, and made of very thin glass. A dozen can be procured for ten or twelve cents at any place where chemical supplies are to be found. A short tallow candle, held in a cheap tin candlestick, answers for the flame; and the tobacco-pipe, converted into the blowpipe just described, can be used in any of the experiments here given. Take a piece of a broken window pane, hold it in the left hand very near the candle flame, then holding the blowpipe so that the shorter end nearly touches the flame, blow steadily through the pipe-stem a current of air into the flame, which sends it upon the glass and soon reduces the part in contact with it to a red-hot melting mass; this can be worked into various shapes by forming it with the aid of pincers; or it can easily be joined to pieces of different colors, by holding the two together and turning the full force of the blaze upon them.
The little tubes may be heated in the same manner, and one end be closed air tight, by pinching it tightly while still hot; then, after heating the portion near the end to a red heat, lay the blowpipe aside, and, taking the tube away from the flame, blow into the open end with the mouth. If this is done quickly, before the glass has had time to cool, a pretty bubble or balloon is the result.
A SIPHON.
A simple glass siphon can be made by taking one of the above tubes and heating it at a point about one-third of its length from the end, till the surface appears a rosy red; then carefully bending it over the round part of a clothes-pin, till the two ends form parallel lines.
A simple experiment with the siphon affords considerable amusement to the little folks, and is well worth trying. Take two tumblers, place them side by side, and fill one with water. Now fill the siphon with water and place the longer end in the empty tumbler, and the shorter one well down in the water of the other. Immediately the laborer will begin to work, pumping water into the empty vessel, and will not stop until he has reduced the water in the full tumbler to a level with the end of the tube.
TO MELT STONES.
Many kinds of stones containing more or less metallic ores, can be readily melted by means of the blowpipe. When the specimens are small they can be placed upon a piece of mica, and then presented to the flame; or a clay receptacle can be made for the purpose, by simply hollowing out a small cavity in one side of a lump of clay. Large ones can be held in the hand or with the pincers as in the case of the glass melting.
A SOAP BUBBLE.
Within the past few years soap-bubble parties have been quite the style among our young people, and not a few of the older members of society have joined in the frolic with as much zest as their younger competitors. Usually at such gatherings, after the guests have all arrived, the hostess, having previously secured two or three boxes of bonbons, or other equally inexpensive trifles for prizes, presents each of her guests with an ordinary clay pipe, and leading the way to the room in which the bowls of soap-suds are already prepared, shows her prizes, and challenges all to the contest. If fine, large iridescent bubbles are desired, it is well to add a small quantity of glycerine to the water used. It is said that if the mixture of glycerine and water is allowed to stand some hours before it is used the effect is much better. Hot water and soap can be added just before the party enter, and only two bowls of the soap mixture are necessary for quite a large party. These should be placed upon small side tables or stands at opposite ends of the room. Two or three reliable persons should be chosen for judges to decide the contest. The parents or some older members of the family, at whose house the party is held, usually perform this duty. I should have added, when speaking of the soap mixture, that the common yellow soap intended for laundry use, is much better for this purpose than the finer toilet varieties most commonly used by amateur soap-bubble blowers.
RESIN BUBBLES.
If the end of a tobacco-pipe be dipped in melted resin, at a temperature a little above that of boiling water, taken out, and held nearly in a vertical position and blown through, bubbles will be formed of all possible sizes, from that of a hen’s egg, down to sizes which can hardly be discerned by the naked eye, and from their silvery luster, and reflection of the different rays of light, they have a pleasing appearance. Some that have been formed these eight months, are as perfect as when first made. They generally assume the form of a string of beads, many of them perfectly regular, and connected by a very fine fiber, but the production is never twice alike. If expanded over a gas jet by means of a small rubber tube, they would probably float around the upper part of the room.
THE THREE MAGICAL CARDS.
Take three cards of the same size, and thick enough to prevent the black surface from showing through; ink or paint over the whole of one side of c, having the other side perfectly white, and the others, a and b, in the parts shown in Fig. 1; they are now ready for use.
Fig. 2 shows the first arrangement of them, a and b lapping over each other so that when c is placed in the position shown by dotted lines the whole face presents a perfectly white surface. Show this to your audience; then, still holding them in sight, inform them in a neat little speech, that by aid of some magic power you possess, you can readily change these same cards to black, or back again, at will. Now holding them with their backs away from you, in such a manner that the card c cannot be seen by the other boys, turn them upside down and spread out what were the lower parts of a and b. You have them now in the position indicated by Fig. 3, and after carefully turning c you will find them presenting a uniformly black surface. Should any bit of white show at the lower corner, cover it with your thumb. When they are arranged to your satisfaction, hold them up in front of you, and while saying over some cabalistic words, such as, for instance, “Presto, agramento, calafesto—change!” blow upon their faces and turn them around to your audience, which will probably be greatly surprised at this undeniable evidence of your magic skill.
Instead of white, the ordinary playing cards may be used, blacking the back of one to represent c. These are much more showy than the plain white ones, and the trick is not so easily discovered if slight bits of black are seen, as those having black spots are generally taken for the purpose.
One day a little fellow who had been repeatedly mystified by this trick, saw the cards which his brother had prepared lying on the table. He took them up, examined them carefully for a moment, then, with his little face all aglow at the revelation, he exclaimed, “Ha! I’ve found out how you do it now, you just blow charcoal on the other part.” How he got rid of the part already black, he did not explain, nor did we think to ask him, but he had at last solved the puzzle of their turning black, and that was all he cared to do at the time.
AN OPTICAL GAME.
Hold a ring between thumb and forefinger at some distance from the boy addressed, and giving him a crooked stick, ask him to close one eye and try to catch the ring on the stick. This game looks so very simple, that any boy is certain he can do it at one thrust, and is only made aware of its difficulties after several unsuccessful attempts.
TO TELL THE NUMBER THOUGHT OF BY A PERSON.
Desire the person who has thought of a number to triple it, and to take the exact half of that; triple that half if the number was even, or if odd multiply the larger half by 3; and ask him how many times that answer contains nine: for the answer will contain the double of that number of nines, and one more if it be odd. Thus if the number thought of is 5, its triple will be 15, which cannot be divided by 2 without a remainder. The greater half of 15 is 8. If we multiply this by 3 we have 24, which contains 9 twice. So we shall have 2 + 2 + 1 = 5, the number first thought of.
THE COUNTER PUZZLE.
In an old book published over half a century ago, I came across this puzzle; and finding it gave an evening’s entertainment to our young folks, I introduce it here for the benefit of those boys who take especial delight in games of an arithmetical nature.
Out of thin cardboard—old business cards answer this purpose nicely—make thirty-two blank counters, the size of a dime. Then upon a piece of note-paper mark off a figure just three inches square, and divide it by lines into nine compartments, each containing one square inch. The puzzle is, to arrange the counters in the external cells of the square four different times, and each time to have nine in a row, yet to have the sum of the counters different, and varying from twenty to thirty-two. If you will inspect the following figures you will see how this is possible: the first represents the original disposition of the counters in the cells of the square; the second, that of the same counters when four are taken away; the third, the manner in which they must be disposed when these four are brought back with four others; and the fourth with the addition of four more. There are always nine in each external row, and yet in the first case the whole number is twenty-four, in the second it is twenty, in the third twenty-eight, and in the fourth thirty-two. The numbers are substituted in the place of the counters in the above figures for convenience, but Fig. 5 represents the disposition of the counters, as indicated in Fig. 2.
ANOTHER ARITHMETICAL TRICK.
By knowing the last figure of the product of any two numbers, to tell the other figures. If the number seventy-three be multiplied by each of the numbers in the following arithmetical progression, 3, 6, 9, 12, 15, 18, 21, 24, 27, the products will terminate with the nine digits, in this order, 9, 8, 7, 6, 5, 4, 3, 2, 1; the numbers themselves being as follows: 219, 438, 657, 876, 1095, 1314, 1533, 1752, and 1971. Let, therefore, a little bag be provided, consisting of two partitions, into one of which put several tickets, marked with the number 73, and into the other put as many tickets, 3, 6, 9, etc., up to 27. Then open that part of the bag containing the number 73, and ask a person to take out one ticket only; after which, dexterously change the opening, and desire another person to take a ticket from the other part. Let them now multiply their two numbers together, and tell you the last figure of the product, by which you will readily determine from the foregoing series what the remaining figures must be. Suppose, for example, the numbers taken out of the bag were 73 and 12, then as the product of these two numbers, which is 876, has 6 for its last figure, you will readily know it is the fourth of the series and the other two figures must be 8 and 7.
TO TELL TWO OR MORE NUMBERS WHICH A PERSON HAS THOUGHT OF.
These numbers must not exceed 9. Let him think of two or three numbers, double the first and add 1 to the product, multiply the whole by 5, and add to that product the second number. If there be a third, make him double the first sum and add 1 to it; then desire him to multiple the new sum by 5, and to add to it the third number. If there should be a fourth number, you must proceed in the same manner, desiring him to double the preceding sum, to add 1 to it, to multiply by 5, and then to add the fourth number, and so on. Then ask the number arising from the addition of the last number thought of, and if there were two numbers subtract 5 from it: if three, 55; if four, 555, and so on, for the remainder will be composed of figures, of which the first on the left will be the first number thought of, the next the second, and so of the rest.
Suppose the numbers thought of to be 3, 4, 6; by adding 1 to 6, the double of the first, we have 7, which being multiplied by 5 gives 35; if 4, the second number thought of, be then added, we shall have 39, which doubled gives 78, and if we add 1, and multiply 79 by 5, the result will be 395. Lastly, if we add 6, the third number thought of, the sum will be 401, and if 55 be deducted from it we shall have for the remainder 346, the figures of which 3, 4, and 6, indicate in order the three numbers thought of.