Two of the tallest players represent a bridge by facing each other, clasping hands, and holding them high for the others to pass under. The other players, in a long line, each holding the other by the hand or dress, pass under the arch while the verses are sung alternately by the players representing the bridge and those passing under, those forming the arch singing the first and alternate verses and the last "Off to prison." As the words

"Here's a prisoner I have got,"

are sung, the players representing the bridge drop their arms around the one who happens to be passing under at the time. The succeeding verses are then sung to "Off to prison he must go." During this last one the prisoner is led off to one side to a place supposed to be a prison, and is there asked in a whisper or low voice to choose between two valuable objects, represented by the two bridge players, who have previously agreed which each shall represent, such as a "diamond necklace" or a "gold piano." The prisoner belongs to the side which he thus chooses. When all have been caught the prisoners line up behind their respective leaders (who have up to this time been the holders of the bridge), clasp each other around the waist, and a tug of war takes place, the side winning which succeeds in pulling its opponent across a given line.

Where a large number of players are taking part, say over ten, the action may be made much more rapid and interesting by forming several spans or arches to the bridge instead of only one, and by having the players run instead of walk under. There is thus much more activity for each player, and the prisoners are all caught much sooner.

SINGING GAMES FOR SMALL CHILDREN

MOON AND MORNING STARS

This is a Spanish game. A player represents the moon; the rest are stars. The moon is placed in the shadow of a tree or house.

The morning stars dance about a child, standing on a chair with extended arms, to represent the sun just risen. The stars dance around the sun, occasionally going quite near the moon; while doing this, they sing

O moon and morning stars, O the moon and morning stars Who dares to tread—oh, Within the shadow?

The moon tries to catch a star, and the one caught becomes the moon.

WEE BOLOGNA MAN

Two to forty players. The leader recites:

I'm a wee Bologna Man; Always do the best you can To follow the wee Bologna Man.

While doing this he imitates an instrument of an orchestra. The others imitate him.

This game may be varied, the Bologna man imitating animals or birds, or making any sound he wishes to make, or he can hop and croak like a frog, or imitate the motions and noise of an angry cat, or the like.

DRAW A BUCKET OF WATER

This game is played in groups of four. Two players face each other, clasping hands at full arms' length. The other two face each other in the same way, with their arms crossing those of the first couple at right angles. Bracing the feet, the couples sway backward and forward, singing the following rhyme:

Draw a bucket of water, For my lady's daughter. One in a rush, Two in a rush, Please, little girl, bob under the bush.

When the last line is sung the players all raise their arms without unclasping the hands, and place them around their companions, who stoop to step inside. They will then be standing in a circle with arms around each other's waists. The game finishes by dancing in this position around the ring, repeating the verse once more.



CHAPTER XX GAMES OF ARITHMETIC

THOUGHT NUMBERS—MYSTICAL NINE—MAGIC HUNDRED—KING AND COUNSELLOR— HORSE-SHOE NAILS—DINNER PARTY PUZZLE—BASKETS AND STONES, ETC.

HOW TO TELL ANY NUMBER THOUGHT OF

Ask any person to think of a number, say a certain number of dollars; tell him to borrow that sum of some one in the company, and add the number borrowed to the amount thought of. It will here be proper to name the person who lends him the money, and to beg the one who makes the calculation to do it with great care, as he may readily fall into an error, especially the first time. Then say to the person: "I do not lend you, but give you $10; add them to the former sum." Continue in this manner: "Give the half to the poor, and retain in your memory the other half." Then add: "Return to the gentleman, or lady, what you borrowed, and remember that the sum lent you was exactly equal to the number thought of." Ask the person if he knows exactly what remains; he will answer "Yes". You must then say: "And I know also the number that remains; it is equal to what I am going to conceal in my hand." Put into one of your hands 5 pieces of money, and desire the person to tell how many you have got. He will answer 5; upon which open your hand and show him the 5 pieces. You may then say: "I well knew that your result was 5; but if you had thought of a very large number, for example, two or three millions, the result would have been much greater, but my hand would not have held a number of pieces equal to the remainder." The person then supposing that the result of the calculation must be different, according to the difference of the number thought of, will imagine that it is necessary to know the last number in order to guess the result; but this idea is false, for, in the case which we have here supposed, whatever be the number thought of, the remainder must always be 5. The reason of this is as follows: The sum, the half of which is given to the poor, is nothing else than twice the number thought of, plus 10; and when the poor have received their part, there remains only the number thought of plus 5; but the number thought of is cut off when the sum borrowed is returned, and consequently there remains only 5. The result may be easily known, since it will be the half of the number given in the third part of the operation; for example, whatever be the number thought of, the remainder will be 36 or 25, according as 72 or 50 have been given. If this trick be performed several times successively, the number given in the third part of the operation must be always different; for if the result were several times the same, the deception might be discovered. When the five first parts of the calculation for obtaining a result are finished, it will be best not to name it at first, but to continue the operation, to render it more complex, by saying for example: "Double the remainder, deduct two, add three, take the fourth part," etc.; and the different steps of the calculation may be kept in mind, in order to know how much the first result has been increased or diminished. This irregular process never fails to confound those who attempt to follow it.

ANOTHER WAY

Tell the person to take 1 from the number thought of, and then double the remainder; desire him to take 1 from this double, and to add to it the number thought of, in the last place, ask him the number arising from this addition, and, if you add 3 to it, the third of the sum will be the number thought of. The application of this rule is so easy that it is needless to illustrate it by an example.

A THIRD WAY

Ask the person to add 1 to the triple of the number thought of, and to multiply the sum by three; then bid him add to this product the number thought of, and the result will be a sum from which if 3 be subtracted, the remainder will be ten times the number required; and if the cipher on the right be cut off from the remainder, the other figure will indicate the number sought.

Example—Let the number thought of be 6, the triple of which is 18; and if 1 be added, it makes 19; the triple of this last number is 57, and if 6 be added it makes 63, from which if 3 be subtracted, the remainder will be 60; now, if the cipher on the right be cut off, the remaining figure, 6, will be the number required.

A FOURTH WAY

Tell the person to multiply the number thought of by itself; then desire him to add 1 to the number thought of, and to multiply it also by itself; in the last place, ask him to tell the difference of these two products, which will certainly be an odd number, and the least half of it will be the number required.

Let the number thought of, for example, be 10; which, multiplied by itself, gives 100; in the next place, 10 increased by 1 is 11; which, multiplied by itself makes 121; and the difference of these two squares is 21, the least half of which, being 10, is the number thought of.

HOW TO TELL NUMBERS THOUGHT OF

If one or more numbers thought of be greater than 9, we must distinguish two cases; that in which the number or the numbers thought of is odd, and that in which it is even. In the first case, ask the sum of the first and second; of the second and third; the third and fourth; and so on to the last; and then the sum of the first and the last. Having written down all these sums in order, add together all those, the places of which are odd, as the first, the third, the fifth, etc.; make another sum of all those, the places of which are even, as the second, the fourth, the sixth, etc.; subtract this sum from the former, and the remainder will be the double of the first number. Let us suppose, for example, that the five following numbers are thought of: 3, 7, 13, 17, 20, which, when added two and two as above, give 10, 20, 30, 37, 23; the sum of the first, third, and fifth is 63, and that of the second and fourth is 57; if 57 be subtracted from 63, the remainder 6, will be the double of the first number, 3. Now, if 3 be taken from 10, the first of the sums, the remainder 7, will be the second number; and by proceeding in this manner, we may find all the rest.

In the second case, that is to say, if the number or the numbers thought of be even, you must ask and write down as above, the sum of the first and second; that of the second and third; and so on, as before; but instead of the sum of the first and the last, you must take that of the second and last; then add together those which stand in the even places, and form them into a new sum apart; add also those in the odd places, the first excepted, and subtract this sum from the former, the remainder will be double of the second number; and if the second number, thus found, be subtracted from the sum of the first and second, you will have the first number; if it be taken from that of the second and third, it will give the third; and so of the rest. Let the numbers thought of be, for example, 3, 7, 13, 17; the sums formed as above are 10, 20, 30, 24; the sum of the second and fourth is 44, from which if 30, the third, be subtracted, the remainder will be 14, the double of 7, the second number. The first therefore is 3, third 13, and the fourth 17.

When each of the numbers thought of does not exceed 9, they may be easily found in the following manner:

Having made the person add 1 to the double of the first number thought of, desire him to multiply the whole by 5, and to add to the product the second number. If there be a third, make him double this first sum, and add 1 to it, after which, desire him to multiply the new sum by 5, and to add to it the third number. If there be a fourth, proceed in the same manner, desiring him to double the preceding sum; to add to it 1; to multiply by 5; 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 there were three, 55; if there were 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 second, and so on.

Suppose the numbers thought of be 3, 4, 6; by adding 1 to 6, the double of the first, we shall have 7, which, being multiplied by 5, will give 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, the sum, by 5, the result will be 395. In the last place, if we add 6, the number thought of, the sum will be 401; and if 55 be deducted from it, we shall have, for remainder, 346, the figures of which, 3, 4, 6, indicate in order the three numbers though of.

GOLD AND SILVER GAME

One of the party having in one hand a piece of gold and in the other a piece of silver, you may tell in which hand he has the gold and in which the silver, by the following method: Some value, represented by an even number, such as 8, must be assigned to the gold, and a value represented by an odd number, such as 3, must be assigned to the silver; after which, desire the person to multiply the number in the right hand by any even number whatever, such as 2; and that in the left hand by an odd number, as 3; then bid him add together the two products, and if the whole sum be odd, the gold will be in the right hand and the silver in the left; if the sum be even, the contrary will be the case.

To conceal the trick better, it will be sufficient to ask whether the sum of the two products can be halved without a remainder; for in that case the total will be even, and in the contrary case odd.

It may be readily seen, that the pieces, instead of being in the two hands of the same person, may be supposed to be in the hands of two persons, one of whom has the even number, or piece of gold, and the other the odd number, or piece of silver. The same operations may then be performed in regard to these two persons, as are performed in regard to the two hands of the same person, calling the one privately the right and the other the left.

THE NUMBER BAG

The plan is to let a person select several numbers out of a bag, and to tell him the number which shall exactly divide the sum of those he has chosen; provide a small bag, divided into two parts, into one of which put several tickets, numbered, 6, 9, 15, 36, 63, 120, 213, 309, etc.; and in the other part put as many other tickets marked number 3 only. Draw a handful of tickets from the first part, and, after showing them to the company, put them into the bag again, and, having opened it a second time, desire any one to take out as many tickets as he thinks proper; when he has done that, you open privately the other part of the bag, and tell him to take out of it one ticket only. You may safely pronounce that the ticket shall contain the number by which the amount of the other numbers is divisible; for, as each of these numbers can be multiplied by 3, their sum total must, evidently, be divisible by that number. An ingenious mind may easily diversify this exercise, by marking the tickets in one part of the bag with any numbers that are divisible by 9 only, the properties of both 9 and 3 being the same; and it should never be exhibited to the same company twice without being varied.

THE MYSTICAL NUMBER NINE

The discovery of remarkable properties of the number 9 was accidentally made, more than forty years since, though, we believe, it is not generally known.

The component figures of the product made by the multiplication of every digit into the number 9, when added together, make Nine.

The order of these component figures is reversed after the said number has been multiplied by 5.

The component figures of the amount of the multipliers (viz. 45), when added together, make Nine.

The amount of the several products or multiples of 9 (viz. 405), when divided by 9, gives far a quotient, 45; that is, 4 plus 5 = Nine.

The amount of the first product (viz. 9), when added to the other product, whose respective component figures make 9, is 81; which is the square of Nine.

The said number 81, when added to the above-mentioned amount of the several products, or multiples, of 9 (viz. 405), makes 486; which, if divided by 9, gives, for a quotient, 54; that is 5 plus 4 = Nine.

It is also observable, that the number of changes that may be rung on nine bells, is 362,880; which figures added together, make 27; that is, 2 plus 7 = Nine.

And the quotient of 362,880, divided by 9, will be 40,320; that is, 4 plus 0 plus 3 plus 2 plus 0 = Nine.

To add a figure to any given number, which shall render it divisible by Nine: Add the figures named; and the figure which must be added to the sum produced, in order to render it divisible by 9, is the one required. Thus

Suppose the given number to be 7521: Add these together, and 15 will be produced; now 15 requires 3 to render it divisible by 9; and that number 3, being added to 7521, causes the same divisibility; 7521 plus 3 gives 7524, and divided by 9, gives 836. This exercise may be diversified by your specifying, before the sum is named, the particular place where the figure shall be inserted, to make the number divisible by 9; for it is exactly the same thing whether the figure be put at the head of the number, or between any two of its digits.

THE MAGIC HUNDRED.

Two persons agree to take, alternately, numbers less than a given number, for example, 11 and to add them together till one of them has reached a certain sum, such as 100. By what means can one of them infallibly attain to that number before the other? The whole secret in this consists in immediately making choice of the numbers, 1, 12, 23, 34, and so on, or of a series which continually increases by 11, up to 100. Let us suppose, that the first person, who knows the game, makes choice of 1; it is evident that his adversary, as he must count less than 11, can, at most, reach 11 by adding 10 to it. The first will then take 1, which will make 12; and whatever number the second may add, the first will certainly win, provided he continually add the number which forms the complement of that of his adversary, to 11; that is to say, if the latter take 8, he must take 3; if 9, he must take 2; and so on. By following this method, he will infallibly attain to 89; and it will then be impossible for the second to prevent him from getting first to 100; for whatever number the second takes, he can attain only to 99; after which the first may say—"and 1 makes 100." If the second take 1 after 89, it would make 90, and his adversary would finish by saying—"and 10 makes 100." Between two persons who are equally acquainted with the game, he who begins must necessarily win.

TO GUESS THE MISSING FIGURE

To tell the figure a person has struck out of the sum of two given numbers: Arbitrarily command those numbers only, that are divisible by 9; such, for instance, as 36, 63, 81, 117, 126, 162, 261, 360, 315, and 432. Then let a person choose any two of these numbers; and, after adding them together in his mind, strike out from the sum any one of the figures he pleases. After he has so done, desire him to tell you the sum of the remaining figures; and it follows, that the number which you are obliged to add to this amount, in order to make it 9 or 18, is the one he struck out. Thus:—Suppose he chooses the numbers 162 and 261, making altogether 423, and that he strike out the center figure; the two other figures will, added together, make 7, which, to make nine, requires 2, the number struck out.

THE KING AND THE COUNSELLOR

A King being desirous to confer a liberal reward on one of his courtiers, who had performed some very important service, desired him to ask whatever he thought proper, assuring him it should be granted. The courtier, who was well acquainted with the science of numbers, only requested that the monarch would give him a quantity of wheat equal to that which would arise from one grain doubled sixty-three times successively. The value of the reward was immense; for it will be seen, by calculation, that the sixty-fourth of the double progression divided by 1: 2: 4: 8: 16: 32: etc., is 9223372036854775808. But the sum of all the terms of a double progression, beginning with 1, may be obtained by doubling the last term, and subtracting from it 1. The number of the grains of wheat, therefore, in the present case, will be 18446744073709551615. Now, if a pint contains 9216 grains of wheat, a gallon will contain 73728; and, as eight gallons make one bushel, if we divide the above result by eight times 73728, we shall have 31274997411295 for the number of the bushels of wheat equal to the above number of grains; a quantity greater than what the whole earth could produce in several years.

THE NAILS IN THE HORSE'S SHOE

A man took a fancy to a horse, which a dealer wished to dispose of at as high a price as he could; the latter, to induce the man to become a purchaser, offered to let him have the horse for the value of the twenty-fourth nail in his shoes, reckoning one farthing for the first nail, two for the second, four for the third, and so on to the twenty-fourth. The man, thinking he should have a good bargain, accepted the offer; the price of the horse was, therefore, necessarily great. By calculating as before, the twenty-fourth term of the progression 1:2:4:8: etc., will be found to be 8388608, equal to the number of farthings the purchaser gave for the horse; the price, therefore amounted to 8738 pounds 2s. 8d.

THE DINNER PARTY PUZZLE

A club of seven agreed to dine together every day successively as long as they could sit down to table in different order. How many dinners would be necessary for that purpose? It may be easily found, by the rules already given, that the club must dine together 5040 times, before they would exhaust all the arrangements possible, which would require about thirteen years.

BASKET AND STONES

If a hundred stones be placed in a straight line, at the distance of a yard from each other, the first being at the same distance from a basket, how many yards must the person walk who engages to pick them up, one by one, and put them into the basket? It is evident that, to pick up the first stone, and put it into the basket, the person must walk two yards; for the second, he must walk four; for the third, six; and so on, increasing by two, to the hundredth. The number of yards which the person must walk, will be equal to the sum of the progression, 2, 4, 6, etc., the last term of which is 200, (22). But the sum of the progression is equal to 202, the sum of the two extremes, multiplied by 50, or half the number of terms; that is to say, 10,000 yards, which makes more than 5 1/2 miles.



CHAPTER XXI

ONE HUNDRED CONUNDRUMS

WITTY QUESTIONS-FACETIOUS PUZZLES—READY ANSWERS—ENTERTAINING PLAY UPON WORDS

ONE HUNDRED CONUNDRUMS

He loved her. She hated him, but womanlike, she would have him, and she was the death of him. Who was he? Answer: A flea.

Why is life the greatest of riddles? Because we must all give it up.

If a church be on fire, why has the organ the smallest chance of escape? Because the organ cannot play on it.

Why should a sailor be the best authority as to what goes on in the moon? Because he has been to see (sea).

What does a cat have that no other animal has? Kittens.

When is a man behind the times? When he's a weak (week) back. What is the difference between a baby and a pair of boots? One I was and the other I wear.

Use me well, and I'm everybody; scratch my back and I'm nobody. A looking glass.

What word becomes shorter by adding a syllable to it? Short.

If a stupid fellow was going up for a competitive examination, why should he study the letter P? Because P makes ass Pass.

Why is buttermilk like something that never happened? Because it hasn't a curd (occurred).

Why is the letter O the noisiest of all the vowels? Because the rest are in audible.

Why is a Member of Parliament like a shrimp? Because he has M. P. at the end of his name.

Why is a pig a paradox? Because it is killed first and cured afterward.

Why is a bad half-dollar like something said in a whisper? Because it is uttered, but not allowed (aloud).

Why do black sheep eat less than white ones? Because there are fewer of them.

Why is a barn-door fowl sitting on a gate like a half-penny? Because its head is on one side and its tail on the other.

Why is a man searching for the Philosopher's Stone like Neptune? Because he is a-seeking (sea-king) what never was.

Why is the nose placed in the middle of the face? Because it's the scenter (cen-ter).

What is most like a hen stealing? A cock robbing (cock robin).

What is worse than "raining cats and dogs"? Hailing omnibuses. When is butter like Irish children? When it is made into little pats. Why is a chronometer like thingumbob? Because it's a watch-you-may-call-it.

Of what color is grass when covered with snow? Invisible green.

Name in two letters the destiny of all earthly things? D. K.

What is even better than presence of mind in a railway accident? Absence of body. What word contains all the vowels in due order? Facetiously.

Why is a caterpillar like a hot roll? Because its the grub that makes the butterfly. What is that which occurs twice in a moment, once in a minute, and not once in a thousand years? The letter M.

What is that which will give a cold, cure a cold, and pay the doctor's bill? A draught (draft).

What is that which is neither flesh nor bone, yet has four fingers and a thumb? A glove.

Why has man more hair than woman? Because he is naturally her suitor (hirsuter).

What is that which no one wishes to have, yet no one cares to lose? A bald head.

Why is the letter G like the sun? Because it is the center of light.

Why is the letter D like a wedding-ring? Because we cannot be wed without it.

Why should ladies not learn French? Because one tongue is enough for any woman.

Which tree is most suggestive of kissing? Yew.

What act of folly does a washerwoman commit? Putting out tubs to catch soft water when it rains hard.

Why should a cabman be brave? Because none but the brave deserve the fair (fare).

What is the most difficult surgical operation? To take the jaw out of a woman.

Why is it difficult to flirt on board the P. and O. steamers? Because all of the mails (males) are tied up in bags.

What letter made Queen Bess mind her P's and Q's? R made her (Armada).

Why is it an insult to a cock-sparrow to mistake him for a pheasant? Because it is making game of him.

What is that from which the whole may be taken, and yet some will remain? The word wholesome.

Why is blind-man's buff like sympathy? Because it is a fellow feeling for another.

When may a man be said to have four hands? When he doubles his fists.

Why is it easy to break into an old man's house? Because his gait (gate) is broken and his locks are few.

Why should you not go to New York by the 12:50 train? Because it is ten-to-one if you catch it.

Why should the male sex avoid the letter A? Because it makes the men mean.

When does a man sneeze three times? When he cannot help it.

What relation is the doormat to the scraper? A step farther.

Why does a piebald pony never pay toll? Because his master pays it for him.

Why is the letter S like a sewing-machine? Because it makes needles needless.

What is the difference between a cow and a rickety chair? One gives milk and the other gives way (whey).

What flower most resembles a bull's mouth? A cowslip.

What does a stone become in the water? Wet.

If the alphabet were invited out to dine, what time would U, V, W, X, Y, and Z go—They would go after tea.

When was beef-tea first introduced into England? When Henry VIII dissolved the Pope's bull.

What letter is the pleasantest to a deaf woman? A, because it makes her hear.

When is love a deformity? When it is all on one side.

Why is a mouse like hay? Because the cat'll (cattle) eat it.

Why is a madman equal to two men? Because he is one beside himself.

Why are good resolutions like ladies fainting in church? Because the sooner they are carried out the better.

Which is the merriest letter in the alphabet? U, because it is always in fun.

What is the difference between a bankrupt and a feather bed? One is hard up and the other is soft down.

What is that word of five letters from which, if you take two, only one remains? Stone.

Why is the letter B like a fire? Because it makes oil boil.

What word is pronounced quicker by adding a syllable to it? Quick.

Which animal travels with the most, and which with the least, luggage? The elephant the most because he is never without his trunk. The fox and cock the least because they have only one brush and comb between them.

Why are bakers the most self-denying people? Because they sell what they need (knead) themselves.

Which of the constellations reminds you of an empty fireplace? The Great Bear (grate bear).

What relation is that child to its own father who is not its own father's son? His daughter.

When does a pig become landed property? When he is turned into a meadow.

Which is the heavier, the full or the new moon? The full moon is a great deal lighter.

Why is an alligator the most deceitful of animals? Because he takes you in with an open countenance.

Why are fowls the most profitable of live stock? Because for every grain they give a peck.

What is that which comes with a coach, goes with a coach, is of no use whatever to the coach, and yet the coach can't go without it? Noise.

If your uncle's sister is not your aunt, what relation is she to you? Your mother.

Why does a duck put his head under water? For divers reasons.

Why does it take it out again? For sundry reasons.

What vegetable products are the most important in history? Dates.

Why is the letter W like a maid of honor? Because it is always in waiting.

What letter is always invisible, yet never out of sight? The letter S.

Why is the letter F like a cow's tail? Because it is the end of beef.

On which side of a pitcher is the handle? The outside.

What is higher and handsomer when the head is off? Your pillow.

Why is a pig in a parlor like a house on fire? Because the sooner it is put out the better.

What is the keynote to good breeding? B natural.

What is it that walks with its head downwards? A nail in a shoe.

Why is a lame dog like a schoolboy adding six and seven together? Because he puts down three and carries one.

Why is the Brooklyn Bridge like merit? Because it is very often passed over.

What did Adam first plant in the Garden of Eden? His foot.

What is Majesty, deprived of its externals? A jest.

How would you make a thin man fat? Throw him out of a second story window and let him come down plump.

What is the difference between a young maid of sixteen and an old maid of eighty? One is happy and careless and the other is cappy and hairless.

When was fruit known to use bad language? When the first apple cursed the first pair.

If a man gets up on a donkey, where should he get down? From a swan's breast.

What is lengthened by being cut at both ends? A ditch.

"I am what I am; I am not what I follow. If I were what I follow, I should not be what I am." What is it? A footman.

Which is the strongest day of the week? Sunday. All the others are weak days.

THE END.