Entertainments for Home, Church and School Part 20

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 ill.u.s.trate 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 a.s.signed to the gold, and a value represented by an odd number, such as 3, must be a.s.signed 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 p.r.o.nounce 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.