
MONEY
PUZZLES.
"Put not your trust in money, but
put your money in trust." OLIVER
WENDELL HOLMES.
1.—A
POSTOFFICE PERPLEXITY.
In every business of life we are occasionally perplexed by some chance
question that for the moment staggers us. I quite pitied a young lady in a
branch postoffice when a gentleman entered and deposited a crown on the counter
with this request: "Please give me some twopenny stamps, six times as many penny
stamps, and make up the rest of the money in twopencehalfpenny stamps." For a
moment she seemed bewildered, then her brain cleared, and with a smile she
handed over stamps in exact fulfilment of the order. How long would it have
taken you to think it out?
Solution
2.—YOUTHFUL
PRECOCITY.
The precocity of some youths is surprising. One is disposed to say on
occasion, "That boy of yours is a genius, and he is certain to do great things
when he grows up;" but past experience has taught us that he invariably becomes
quite an ordinary citizen. It is so often the case, on the contrary, that the
dull boy becomes a great man. You never can tell. Nature loves to present to us
these queer paradoxes. It is well known that those wonderful "lightning
calculators," who now and again surprise the world by their feats, lose all
their mysterious powers directly they are taught the elementary rules of
arithmetic.
A boy who was demolishing a choice banana was approached by a young friend,
who, regarding him with envious eyes, asked, "How much did you pay for that
banana, Fred?" The prompt answer was quite remarkable in its way: "The man what
I bought it of receives just half as many sixpences for sixteen dozen dozen
bananas as he gives bananas for a fiver."
Now, how long will it take the reader to say correctly just how much Fred
paid for his rare and refreshing fruit?
Solution
3.—AT
A CATTLE MARKET.
Three countrymen met at a cattle market. "Look here," said Hodge to Jakes,
"I'll give you six of my pigs for one of your horses, and then you'll have twice
as many animals here as I've got." "If that's your way of doing business," said
Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then
you'll have three times as many animals as I." "Well, I'll go better than that,"
said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six
times as many animals as I've got here."
No doubt this was a very primitive way of bartering animals, but it is an
interesting little puzzle to discover just how many animals Jakes, Hodge, and
Durrant must have taken to the cattle market.
Solution
4.—THE
BEANFEAST PUZZLE.
A number of men went out together on a beanfeast. There were four parties
invited—namely, 25 cobblers, 20 tailors, 18 hatters, and 12 glovers. They spent
altogether £6, 13s. It was found that five cobblers spent as much as four
tailors; that twelve tailors spent as much as nine hatters; and that six hatters
spent as much as eight glovers. The puzzle is to find out how much each of the
four parties spent.
Solution
5.—A
QUEER COINCIDENCE.
Seven men, whose names were Adams, Baker, Carter, Dobson, Edwards, Francis,
and Gudgeon, were recently engaged in play. The name of the particular game is
of no consequence. They had agreed that whenever a player won a game he should
double the money of each of the other players—that is, he was to give the
players just as much money as they had already in their pockets. They played
seven games, and, strange to say, each won a game in turn, in the order in which
their names are given. But a more curious coincidence is this—that when they had
finished play each of the seven men had exactly the same amount—two shillings
and eightpence—in his pocket. The puzzle is to find out how much money each man
had with him before he sat down to play.
Solution
6.—A
CHARITABLE BEQUEST.
A man left instructions to his executors to distribute once a year exactly
fiftyfive shillings among the poor of his parish; but they were only to
continue the gift so long as they could make it in different ways, always giving
eighteenpence each to a number of women and half a crown each to men. During how
many years could the charity be administered? Of course, by "different ways" is
meant a different number of men and women every time.
Solution
7.—THE
WIDOW'S LEGACY.
A gentleman who recently died left the sum of £8,000 to be divided among his
widow, five sons, and four daughters. He directed that every son should receive
three times as much as a daughter, and that every daughter should have twice as
much as their mother. What was the widow's share?
Solution
8.—INDISCRIMINATE
CHARITY.
A charitable gentleman, on his way home one night, was appealed to by three
needy persons in succession for assistance. To the first person he gave one
penny more than half the money he had in his pocket; to the second person he
gave twopence more than half the money he then had in his pocket; and to the
third person he handed over threepence more than half of what he had left. On
entering his house he had only one penny in his pocket. Now, can you say exactly
how much money that gentleman had on him when he started for home?
Solution
9.—THE
TWO AEROPLANES.
A man recently bought two aeroplanes, but afterwards found that they would
not answer the purpose for which he wanted them. So he sold them for £600 each,
making a loss of 20 per cent, on one machine and a profit of 20 per cent, on the
other. Did he make a profit on the whole transaction, or a loss? And how
much?
Solution
10.—BUYING
PRESENTS.
"Whom do you think I met in town last week, Brother William?" said Uncle
Benjamin. "That old skinflint Jorkins. His family had been taking him around
buying Christmas presents. He said to me, 'Why cannot the government abolish
Christmas, and make the giving of presents punishable by law? I came out this
morning with a certain amount of money in my pocket, and I find I have spent
just half of it. In fact, if you will believe me, I take home just as many
shillings as I had pounds, and half as many pounds as I had shillings. It is
monstrous!'" Can you say exactly how much money Jorkins had spent on those
presents?
Solution
11.—THE
CYCLISTS' FEAST.
'Twas last Bank Holiday, so I've been
told, Some cyclists rode abroad in glorious
weather. Resting at noon within a tavern
old, They all agreed to have a feast
together. "Put it all in one bill, mine host," they
said, "For every man an equal share will
pay." The bill was promptly on the table
laid, And four pounds was the reckoning that
day. But, sad to state, when they prepared to
square, 'Twas found that two had sneaked outside and
fled. So, for two shillings more than his due
share Each honest man who had remained was
bled. They settled later with those rogues, no
doubt. How many were they when they first set
out?
Solution
12.—A
QUEER THING IN MONEY.
It will be found that £66, 6s. 6d. equals 15,918 pence. Now,
the four 6's added together make 24, and the figures in 15,918 also add to 24.
It is a curious fact that there is only one other sum of money, in pounds,
shillings, and pence (all similarly repetitions of one figure), of which the
digits shall add up the same as the digits of the amount in pence. What is the
other sum of money?
Solution
13.—A
NEW MONEY PUZZLE.
The largest sum of money that can be written in pounds, shillings, pence, and
farthings, using each of the nine digits once and only once, is £98,765, 4s.
3½d. Now, try to discover the smallest sum of money that can be written
down under precisely the same conditions. There must be some value given for
each denomination—pounds, shillings, pence, and farthings—and the nought may not
be used. It requires just a little judgment and thought.
Solution
14.—SQUARE
MONEY.
"This is queer," said McCrank to his friend. "Twopence added to twopence is
fourpence, and twopence multiplied by twopence is also fourpence." Of course, he
was wrong in thinking you can multiply money by money. The multiplier must be
regarded as an abstract number. It is true that two feet multiplied by two feet
will make four square feet. Similarly, two pence multiplied by two pence will
produce four square pence! And it will perplex the reader to say what a "square
penny" is. But we will assume for the purposes of our puzzle that twopence
multiplied by twopence is fourpence. Now, what two amounts of money will produce
the next smallest possible result, the same in both cases, when added or
multiplied in this manner? The two amounts need not be alike, but they must be
those that can be paid in current coins of the realm.
Solution
15.—POCKET
MONEY.
What is the largest sum of money—all in current silver coins and no
fourshilling piece—that I could have in my pocket without being able to give
change for a halfsovereign?
Solution
16.—THE
MILLIONAIRE'S PERPLEXITY.
Mr. Morgan G. Bloomgarten, the millionaire, known in the States as the Clam
King, had, for his sins, more money than he knew what to do with. It bored him.
So he determined to persecute some of his poor but happy friends with it. They
had never done him any harm, but he resolved to inoculate them with the "source
of all evil." He therefore proposed to distribute a million dollars among them
and watch them go rapidly to the bad. But he was a man of strange fancies and
superstitions, and it was an inviolable rule with him never to make a gift that
was not either one dollar or some power of seven—such as 7, 49, 343, 2,401,
which numbers of dollars are produced by simply multiplying sevens together.
Another rule of his was that he would never give more than six persons exactly
the same sum. Now, how was he to distribute the 1,000,000 dollars? You may
distribute the money among as many people as you like, under the conditions
given.
Solution
17.—THE
PUZZLING MONEYBOXES.
Four brothers—named John, William, Charles, and Thomas—had each a moneybox.
The boxes were all given to them on the same day, and they at once put what
money they had into them; only, as the boxes were not very large, they first
changed the money into as few coins as possible. After they had done this, they
told one another how much money they had saved, and it was found that if John
had had 2s. more in his box than at present, if William had had
2s. less, if Charles had had twice as much, and if Thomas had had half as
much, they would all have had exactly the same amount.
Now, when I add that all four boxes together contained 45s., and that
there were only six coins in all in them, it becomes an entertaining puzzle to
discover just what coins were in each box.
Solution
18.—THE
MARKET WOMEN.
A number of market women sold their various products at a certain price per
pound (different in every case), and each received the same amount—2s.
2½d. What is the greatest number of women there could have been? The price per
pound in every case must be such as could be paid in current money.
Solution
19.—THE
NEW YEAR'S EVE SUPPERS.
The proprietor of a small London café has given me some interesting figures.
He says that the ladies who come alone to his place for refreshment spend each
on an average eighteenpence, that the unaccompanied men spend half a crown each,
and that when a gentleman brings in a lady he spends half a guinea. On New
Year's Eve he supplied suppers to twentyfive persons, and took five pounds in
all. Now, assuming his averages to have held good in every case, how was his
company made up on that occasion? Of course, only single gentlemen, single
ladies, and pairs (a lady and gentleman) can be supposed to have been present,
as we are not considering larger parties.
Solution
20.—BEEF
AND SAUSAGES.
"A neighbour of mine," said Aunt Jane, "bought a certain quantity of beef at
two shillings a pound, and the same quantity of sausages at eighteenpence a
pound. I pointed out to her that if she had divided the same money equally
between beef and sausages she would have gained two pounds in the total weight.
Can you tell me exactly how much she spent?"
"Of course, it is no business of mine," said Mrs. Sunniborne; "but a lady who
could pay such prices must be somewhat inexperienced in domestic economy."
"I quite agree, my dear," Aunt Jane replied, "but you see that is not the
precise point under discussion, any more than the name and morals of the
tradesman."
Solution
21.—A
DEAL IN APPLES.
I paid a man a shilling for some apples, but they were so small that I made
him throw in two extra apples. I find that made them cost just a penny a dozen
less than the first price he asked. How many apples did I get for my
shilling?
Solution
22.—A
DEAL IN EGGS.
A man went recently into a dairyman's shop to buy eggs. He wanted them of
various qualities. The salesman had newlaid eggs at the high price of
fivepence each, fresh eggs at one penny each, eggs at a halfpenny each, and eggs
for electioneering purposes at a greatly reduced figure, but as there was no
election on at the time the buyer had no use for the last. However, he bought
some of each of the three other kinds and obtained exactly one hundred eggs for
eight and fourpence. Now, as he brought away exactly the same number of eggs of
two of the three qualities, it is an interesting puzzle to determine just how
many he bought at each price.
Solution
23.—THE
CHRISTMASBOXES.
Some years ago a man told me he had spent one hundred English silver coins in
Christmasboxes, giving every person the same amount, and it cost him exactly
£1, 10s. 1d. Can you tell just how many persons received the
present, and how he could have managed the distribution? That odd penny looks
queer, but it is all right.
Solution
24.—A
SHOPPING PERPLEXITY.
Two ladies went into a shop where, through some curious eccentricity, no
change was given, and made purchases amounting together to less than five
shillings. "Do you know," said one lady, "I find I shall require no fewer than
six current coins of the realm to pay for what I have bought." The other lady
considered a moment, and then exclaimed: "By a peculiar coincidence, I am
exactly in the same dilemma." "Then we will pay the two bills together." But, to
their astonishment, they still required six coins. What is the smallest possible
amount of their purchases—both different?
Solution
25.—CHINESE
MONEY.
The Chinese are a curious people, and have strange inverted ways of doing
things. It is said that they use a saw with an upward pressure instead of a
downward one, that they plane a deal board by pulling the tool toward them
instead of pushing it, and that in building a house they first construct the
roof and, having raised that into position, proceed to work downwards. In money
the currency of the country consists of taels of fluctuating value. The tael
became thinner and thinner until 2,000 of them piled together made less than
three inches in height. The common cash consists of brass coins of varying
thicknesses, with a round, square, or triangular hole in the centre, as in our
illustration.
These are strung on wires like buttons. Supposing that eleven coins with
round holes are worth fifteen chingchangs, that eleven with square holes are
worth sixteen chingchangs, and that eleven with triangular holes are worth
seventeen chingchangs, how can a Chinaman give me change for half a crown,
using no coins other than the three mentioned? A chingchang is worth exactly
twopence and fourfifteenths of a chingchang.
Solution
26.—THE
JUNIOR CLERK'S PUZZLE.
Two youths, bearing the pleasant names of Moggs and Snoggs, were employed as
junior clerks by a merchant in Mincing Lane. They were both engaged at the same
salary—that is, commencing at the rate of £50 a year, payable halfyearly. Moggs
had a yearly rise of £10, and Snoggs was offered the same, only he asked, for
reasons that do not concern our puzzle, that he might take his rise at £2,
10s. halfyearly, to which his employer (not, perhaps, unnaturally!) had
no objection.
Now we come to the real point of the puzzle. Moggs put regularly into the
Post Office Savings Bank a certain proportion of his salary, while Snoggs saved
twice as great a proportion of his, and at the end of five years they had
together saved £268, 15s. How much had each saved? The question of
interest can be ignored.
Solution
27.—GIVING
CHANGE.
Every one is familiar with the difficulties that frequently arise over the
giving of change, and how the assistance of a third person with a few coins in
his pocket will sometimes help us to set the matter right. Here is an example.
An Englishman went into a shop in New York and bought goods at a cost of
thirtyfour cents. The only money he had was a dollar, a threecent piece, and a
twocent piece. The tradesman had only a halfdollar and a quarterdollar. But
another customer happened to be present, and when asked to help produced two
dimes, a fivecent piece, a twocent piece, and a onecent piece. How did the
tradesman manage to give change? For the benefit of those readers who are not
familiar with the American coinage, it is only necessary to say that a dollar is
a hundred cents and a dime ten cents. A puzzle of this kind should rarely cause
any difficulty if attacked in a proper manner.
Solution
28.—DEFECTIVE
OBSERVATION.
Our observation of little things is frequently defective, and our memories
very liable to lapse. A certain judge recently remarked in a case that he had no
recollection whatever of putting the weddingring on his wife's finger. Can you
correctly answer these questions without having the coins in sight? On which
side of a penny is the date given? Some people are so unobservant that, although
they are handling the coin nearly every day of their lives, they are at a loss
to answer this simple question. If I lay a penny flat on the table, how many
other pennies can I place around it, every one also lying flat on the table, so
that they all touch the first one? The geometrician will, of course, give the
answer at once, and not need to make any experiment. He will also know that, since all circles are
similar, the same answer will necessarily apply to any coin. The next question
is a most interesting one to ask a company, each person writing down his answer
on a slip of paper, so that no one shall be helped by the answers of others.
What is the greatest number of threepennypieces that may be laid flat on the
surface of a halfcrown, so that no piece lies on another or overlaps the
surface of the halfcrown? It is amazing what a variety of different answers one
gets to this question. Very few people will be found to give the correct number.
Of course the answer must be given without looking at the coins.
Solution
29.—THE
BROKEN COINS.
A man had three coins—a sovereign, a shilling, and a penny—and he found that
exactly the same fraction of each coin had been broken away. Now, assuming that
the original intrinsic value of these coins was the same as their nominal
value—that is, that the sovereign was worth a pound, the shilling worth a
shilling, and the penny worth a penny—what proportion of each coin has been lost
if the value of the three remaining fragments is exactly one pound?
Solution
30.—TWO
QUESTIONS IN PROBABILITIES.
There is perhaps no class of puzzle over which people so frequently blunder
as that which involves what is called the theory of probabilities. I will give
two simple examples of the sort of puzzle I mean. They are really quite easy,
and yet many persons are tripped up by them. A friend recently produced five
pennies and said to me: "In throwing these five pennies at the same time, what
are the chances that at least four of the coins will turn up either all heads or
all tails?" His own solution was quite wrong, but the correct answer ought not
to be hard to discover. Another person got a wrong answer to the following
little puzzle which I heard him propound: "A man placed three sovereigns and one
shilling in a bag. How much should be paid for permission to draw one coin from
it?" It is, of course, understood that you are as likely to draw any one of the
four coins as another.
Solution
31.—DOMESTIC
ECONOMY.
Young Mrs. Perkins, of Putney, writes to me as follows: "I should be very
glad if you could give me the answer to a little sum that has been worrying me a
good deal lately. Here it is: We have only been married a short time, and now,
at the end of two years from the time when we set up housekeeping, my husband
tells me that he finds we have spent a third of his yearly income in rent,
rates, and taxes, onehalf in domestic expenses, and oneninth in other ways. He
has a balance of £190 remaining in the bank. I know this last, because he
accidentally left out his passbook the other day, and I peeped into it. Don't
you think that a husband ought to give his wife his entire confidence in his
money matters? Well, I do; and—will you believe it?—he has never told me what
his income really is, and I want, very naturally, to find out. Can you tell me
what it is from the figures I have given you?"
Yes; the answer can certainly be given from the figures contained in Mrs.
Perkins's letter. And my readers, if not warned, will be practically unanimous
in declaring the income to be—something absurdly in excess of the correct
answer!
Solution
32.—THE
EXCURSION TICKET PUZZLE.
When the big flaming placards were exhibited at the little provincial railway
station, announcing that the Great —— Company would run cheap excursion trains
to London for the Christmas holidays, the inhabitants of MudleycumTurmits were
in quite a flutter of excitement. Half an hour before the train came in the
little booking office was crowded with country passengers, all bent on visiting
their friends in the great Metropolis. The booking clerk was unaccustomed to
dealing with crowds of such a dimension, and he told me afterwards, while wiping
his manly brow, that what caused him so much trouble was the fact that these
rustics paid their fares in such a lot of small money.
He said that he had enough farthings to supply a West End draper with change
for a week, and a sufficient number of threepenny pieces for the congregations
of three parish churches. "That excursion fare," said he, "is nineteen shillings
and ninepence, and I should like to know in just how many different ways it is
possible for such an amount to be paid in the current coin of this realm."
Here, then, is a puzzle: In how many different ways may nineteen shillings
and ninepence be paid in our current coin? Remember that the fourpennypiece is
not now current.
Solution
33.—A
PUZZLE IN REVERSALS.
Most people know that if you take any sum of money in pounds, shillings, and
pence, in which the number of pounds (less than £12) exceeds that of the pence,
reverse it (calling the pounds pence and the pence pounds), find the difference,
then reverse and add this difference, the result is always £12, 18s.
11d. But if we omit the condition, "less than £12," and allow nought to
represent shillings or pence—(1) What is the lowest amount to which the rule
will not apply? (2) What is the highest amount to which it will apply? Of
course, when reversing such a sum as £14, 15s. 3d. it may be
written £3, 16s. 2d., which is the same as £3, 15s.
14d.
Solution
34.—THE
GROCER AND DRAPER.
A country "grocer and draper" had two rival assistants, who prided themselves
on their rapidity in serving customers. The young man on the grocery side could
weigh up two onepound parcels of sugar per minute, while the drapery assistant
could cut three oneyard lengths of cloth in the same time. Their employer, one
slack day, set them a race, giving the grocer a barrel of sugar and telling him to weigh up
fortyeight onepound parcels of sugar While the draper divided a roll of
fortyeight yards of cloth into yard pieces. The two men were interrupted
together by customers for nine minutes, but the draper was disturbed seventeen
times as long as the grocer. What was the result of the race?
Solution
35.—JUDKINS'S
CATTLE.
Hiram B. Judkins, a cattledealer of Texas, had five droves of animals,
consisting of oxen, pigs, and sheep, with the same number of animals in each
drove. One morning he sold all that he had to eight dealers. Each dealer bought
the same number of animals, paying seventeen dollars for each ox, four dollars
for each pig, and two dollars for each sheep; and Hiram received in all three
hundred and one dollars. What is the greatest number of animals he could have
had? And how many would there be of each kind?
Solution
36.—BUYING
APPLES.
As the purchase of apples in small quantities has always presented
considerable difficulties, I think it well to offer a few remarks on this
subject. We all know the story of the smart boy who, on being told by the old
woman that she was selling her apples at four for threepence, said: "Let me see!
Four for threepence; that's three for twopence, two for a penny, one for
nothing—I'll take one!"
There are similar cases of perplexity. For example, a boy once picked up a
penny apple from a stall, but when he learnt that the woman's pears were the
same price he exchanged it, and was about to walk off. "Stop!" said the woman.
"You haven't paid me for the pear!" "No," said the boy, "of course not. I gave
you the apple for it." "But you didn't pay for the apple!" "Bless the woman! You
don't expect me to pay for the apple and the pear too!" And before the poor
creature could get out of the tangle the boy had disappeared.
Then, again, we have the case of the man who gave a boy sixpence and promised
to repeat the gift as soon as the youngster had made it into ninepence. Five
minutes later the boy returned. "I have made it into ninepence," he said, at the
same time handing his benefactor threepence. "How do you make that out?" he was
asked. "I bought threepennyworth of apples." "But that does not make it into
ninepence!" "I should rather think it did," was the boy's reply. "The apple
woman has threepence, hasn't she? Very well, I have threepennyworth of apples,
and I have just given you the other threepence. What's that but ninepence?"
I cite these cases just to show that the small boy really stands in need of a
little instruction in the art of buying apples. So I will give a simple poser
dealing with this branch of commerce.
An old woman had apples of three sizes for sale—one a penny, two a penny, and
three a penny. Of course two of the second size and three of the third size were
respectively equal to one apple of the largest size. Now, a gentleman who had an
equal number of boys and girls gave his children sevenpence to be spent amongst
them all on these apples. The puzzle is to give each child an equal distribution
of apples. How was the sevenpence spent, and how many children were there?
Solution
37.—BUYING
CHESTNUTS.
Though the following little puzzle deals with the purchase of chestnuts, it
is not itself of the "chestnut" type. It is quite new. At first sight it has
certainly the appearance of being of the "nonsense puzzle" character, but it is
all right when properly considered.
A man went to a shop to buy chestnuts. He said he wanted a pennyworth, and
was given five chestnuts. "It is not enough; I ought to have a sixth," he
remarked! "But if I give you one chestnut more." the shopman replied, "you will
have five too many." Now, strange to say, they were both right. How many
chestnuts should the buyer receive for half a crown?
Solution
38.—THE
BICYCLE THIEF.
Here is a little tangle that is perpetually cropping up in various guises. A
cyclist bought a bicycle for £15 and gave in payment a cheque for £25. The
seller went to a neighbouring shopkeeper and got him to change the cheque for
him, and the cyclist, having received his £10 change, mounted the machine and
disappeared. The cheque proved to be valueless, and the salesman was requested
by his neighbour to refund the amount he had received. To do this, he was
compelled to borrow the £25 from a friend, as the cyclist forgot to leave his
address, and could not be found. Now, as the bicycle cost the salesman £11, how
much money did he lose altogether?
Solution
39.—THE
COSTERMONGER'S PUZZLE.
"How much did yer pay for them oranges, Bill?"
"I ain't agoin' to tell yer, Jim. But I beat the old cove down fourpence a
hundred."
"What good did that do yer?"
"Well, it meant five more oranges on every ten shillin'sworth."
Now, what price did Bill actually pay for the oranges? There is only one rate
that will fit in with his statements.
Solution
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