Books: Entertainments for Home, Church and School
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Frederica Seeger >> Entertainments for Home, Church and School
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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.
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