Henry Ernest Dudeney/Puzzles and Curious Problems/Arithmetical and Algebraical Problems/Money Puzzles

Henry Ernest Dudeney: Puzzles and Curious Problems: Arithmetical and Algebraical Problems

$1$ - The Money Bag

"A bag," said Rackbrane, when helping himself to the marmalade, "contained fifty-five coins consisting entirely of crowns and shillings,

and their total value was $\pounds 7, \ 3 \shillings 0 \oldpence$

How many coins were there of each kind?"

$2$ - A Legacy Puzzle

A man left legacies to his three sons and to a hospital, amounting in all to $\pounds 1,320$.

If he had left the hospital legacy also to his first son, that son would have received as much as the other two sons together.

If he had left it to his second son, that son would have received twice as much as the other two sons together.

If he had left the hospital legacy to his third son, he would have received then thrice as much as the first son and second son together.

Find the amount of each legacy.

$3$ - Buying Toys

George and William were sent out to buy toys for the family Christmas tree,

and, unknown to each other, both went at different times to the same little shop,

where they had sold all their stock of small toys

except engines at $4 \oldpence$, balls at $3 \oldpence$ each, dolls at $2 \oldpence$ each, and trumpets at $\tfrac 1 2 \oldpence$ each.

They both bought some of all, and obtained $21$ articles, spending $2 \shillings$ each.

But William bought more trumpets than George.

What were their purchases?

$4$ - Puzzling Legacies

A man bequeathed a sum of money, a little less than $\pounds 1500$, to be divided as follows:

The five children and the lawyer received such sums that

the square root of the eldest son's share,

the second son's share divided by two,

the third son's share minus $\pounds 2$,

the fourth son's share plus $\pounds 2$,

the daughter's share multiplied by two,

and the square of the lawyer's fee

all worked out at exactly the same sum of money.

No pounds were divided, and no money was left over after the division.

What was the total amount bequeathed?

$5$ - Dividing the Legacy

A man left $\pounds 100$ to be divided between his two sons Alfred and Benjamin.

If one-third of Alfred's legacy be taken from one-fourth of Benjamin's, the remainder would be $\pounds 11$.

What was the amount of each legacy?

$6$ - A New Partner

Two partners named Smugg and Williamson have decided to take a Mr. Rogers into partnership.

Smugg has one and a half times as much capital invested in the business as Williamson

and Rogers has to pay down $\pounds 2500$, which sum shall be divided between Smugg and Williamson,

so that the three partners shall have an equal interest in the business.

How shall that sum be divided?

$7$ - Squaring Pocket-Money

A man has four different English coins in his pocket,

and their sum in pence was a square number.

He spent one of the coins, and the sum of the remainder in shillings was a square number.

He then spent one of the three, and the sum of the other two in pence was a square number.

And when he deducted the number of farthings in one of them from the number of halfpennies in the other, the remainder was a square number.

What were the coins?

$8$ - Equal Values

A lady and her daughter set out on a walk the other day,

and happened to notice that they both had money of the same value in their purses,

consisting of three coins each, and all six coins were different.

During the afternoon they made slight purchases,

and on returning home found that they again had similar value in their purses made up of three coins each, and all six different.

How much money did they set out with, and what was the value of their purchases?

$9$ - Pocket-Money

"When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash.

I spend just one-half of what I had on my railway ticket, and then bought a penny newspaper.

When I got to the terminus I spent half of what I had left and twopence more on a telegram.

Then I spent half of the remainder on a bus, and gave threepence to that old match-seller outside the club.

Consequently I arrive here with this single penny.

Now, how much did I start out with?"

$10$ - Mental Arithmetic

If a tobacconist offers a cigar at $7 \tfrac 3 4 \oldpence$,

but says we can have the box of $100$ for $65 \shillings$,

shall we save much by buying the box?

In other words, what would $100$ at $7 \tfrac 3 4 \oldpence$ cost?

By a little rule that we shall give the calculation takes only a few moments.

$11$ - Distribution

Nine persons in a party, $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $K$, did as follows:

First $A$ gave each of the others as much money as he (the receiver) already held;

then $B$ did the same; then $C$; and so on to the last,

$K$ giving to each of the other eight persons the amount the receiver then held.

Then it was found that each of the nine persons held the same amount.

Can you find the smallest amount in pence that each person could have originally held?

$12$ - Reductions in Price

"I have often been mystified," said Colonel Crackham, "at the startling reductions some people make in their prices,

and wondered on what principles they went to work.

For example, a man offered me a motor-car two years ago for $\pounds 512$;

a year later his price was $\pounds 320$;

a little while after he asked a level $\pounds 200$;

and last week he was willing to sell for $\pounds 125$.

The next time he reduces I shall buy.

At what price shall I purchase if he makes a consistent reduction?"

$13$ - The Three Hospitals

Colonel Crackham said that a hospital collection brought in the following contributions:

A cheque for $\pounds 2, 10 \shillings$,

two cheques for $\pounds 1, 5 \shillings$ each,

three $\pounds 1$ Treasury notes,

three $10 \shillings$ Treasury notes,

two crowns,

two postal orders for $3 \shillings$ each,

two florins,

and three shillings.

As this money had to be divided amongst three hospitals, just as it stood,

since nobody happened to have any change in his pocket,

how was it to be done?

$14$ - Horses and Bullocks

A dealer bought a number of horses at $\pounds 17, 4 \shillings$ each,

and a number of bullocks at $\pounds 13, 5 \shillings$ each.

He then discovered that the horses had cost him in all $33 \shillings$ more than the bullocks.

Now, what is the smallest number of each that he must have bought?

$15$ - Buying Turkeys

A man bought a number of turkeys at a cost of $\pounds 60$,

and after reserving fifteen of the birds he sold the remainder for $\pounds 54$,

thus gaining $2 \shillings$ a head by these.

How may turkeys did he buy?

$16$ - The Thrifty Grocer

A grocer in a small way of business had managed to put aside (apart from his legitimate profits) a little sum in $\pounds 1$ notes, $10 \shillings$ notes, and crowns,

which he kept in eight bags,

there being the same number of crowns and of each kind of note in each bag.

One night he decided to put the money into only seven bags, again with the same number of each kind of currency in every bag.

And the following night he further reduced the number of bags to six, again putting the same number of each kind of note and of crowns in every bag.

The next night the poor demented miser tried to do the same with five bags, but after hours of trial he utterly failed, had a fit, and died, greatly respected by his neighbours.

What is the smallest possible amount of money he had put aside?

$17$ - The Missing Penny

Two market women were selling their apples, one at three a penny and the other at two a penny.

One day they were both called away when each had thirty apples unsold:

these they handed to a friend to sell at five for twopence.

Now it will be seen that if they had sold their apples separately they would have fetched $2 \shillings 1 \oldpence$,

but when they were sold together they fetched only $2 \shillings$

Can you explain this little mystery?

$18$ - The Red Death League

In a story too tedious to relate, we are given to find the number of members and cost of membership when the total subscription is $\pounds 323, 5 \shillings 4 \tfrac 1 4 \oldpence$

We are also given that the number of members is under $500$.

$19$ - A Poultry Poser

Three chickens and one duck sold for as much as two geese;

one chicken, two ducks, and three geese were sold together for $25 \shillings$

What was the price of each bird in an exact number of shillings?

$20$ - Boys and Girls

Nine boys and three girls agreed to share equally their pocket-money.

every boy gave an equal sum to every girl,

and every girl gave another equal sum to every boy.

Every child then possessed exactly the same amount.

What was the smallest possible amount that each then possessed?

$21$ - The Cost of a Suit

Melville bought a suit.

The jacket cost as much as the trousers and waistcoat.

The jacket and two pairs of trousers would cost $\pounds 7, 17 \shillings 6 \oldpence$

The trousers and two waistcoats would cost $\pounds 4, 10 \shillings$

Can you tell me the cost of the suit?

$22$ - The War Horse

Farmer Wurzel bought a old war horse for $\pounds 13$ and sold it later for $\pounds 30$.

After having paid for its keep, it turned out he lost half the price he paid and one-quarter the cost of his keep.

How much did Farmer Wurzel lose on the transaction?

$23$ - A Deal in Cucumbers

"How much to you pay for these cucumbers?" someone asked.

The reply: "I pay as many shillings for six dozen cucumbers of that size as I get cucumbers for $32 \shillings$"

What was the price per cucumber?

$24$ - The Two Turkeys

"I sold those two turkeys," said Tozer.

"They weighed $20$ pounds together.

Mrs. Burkett paid $24 \shillings 8 \oldpence$ for the large one, and Mrs. Suggs paid $6 \shillings 10 \oldpence$ for the small one.

I made $2 \oldpence$ a pound more on the little one than on the other."

What did the big one weigh?

$25$ - Flooring Figures

A correspondent accidentally discovered the following when making out an invoice with the items:

$148 \ \mathrm {ft.}$ flooring boards at $2 \oldpence$ $\pounds 1, 4 \shillings 8 \oldpence$

$150 \ \mathrm {ft.}$ flooring boards at $2 \oldpence$ $\pounds 1, 5 \shillings 0 \oldpence$

where it will be seen that in each case the three digits are repeated in the same order.

He thought this coincidence so extraordinary that he tried to find another similar case.

This seems to have floored him. But it is possible.

$26$ - Cross and Coins

Take any $11$ of the $12$ current coins of the realm,

and using one duplicate coin, can you place the $12$ coins, one in each division of the cross,

so that they add up to the same value in the upright and in the horizontal?

$27$ - Buying Tobacco

A box of $50$ cigarettes cost the same in shillings and pence as some tobacco bought in pence and shillings.

The change out of a $10 \shillings$ note was the same as the cost of the cigarettes.

What did the cigarettes cost?

$28$ - A Farthings Puzzle

Find a sum of money expressed in pounds, shillings and pence

which, when you take the currency indicators and punctuation away, reads the number that you get when you reduce the sum to farthings.

$29$ - The Shopkeeper's Puzzle

A shopkeeper uses a code word where each letter stands for the digits from $0$ to $9$.

What is the code used to encode this addition sum?

  GAUNT
+ OILER
 ------
 RGUOEI

$30$ - Subscriptions

Seven men agreed to subscribe towards a certain fund,

and the first six gave $\pounds 10$ each.

The other man gave $\pounds 3$ more than the average of the seven.

What amount did the seventh man subscribe?

$31$ - A Queer Settling Up

Person 1: "Here is my purse, give me just as much money as you find in it."

Person 2, having done that: "If you give me as much as I have left of my own, we shall be square."

After Person 2 has done that, Person 1 find his purse contains three shillings and sixpence,

while Person 2 has three shillings.

How much did each possess at the start?

$32$ - Apple Transactions

A man was asked what price per $100$ he paid for some apples, and his reply was as follows:

"If they had been $4 \oldpence$ more per $100$ I should have got $5$ less for $10 \shillings$"

Can you say what was the price per $100$?

$33$ - Prosperous Business

A man started business with a capital of $\pounds 2000$, and increased his wealth by $50$ per cent every three years.

How much did he possess at the expiration of eighteen years?

$34$ - The Banker and the Note

A banker in a country town was walking down the street when he saw a $\pounds 5$ note on the kerb-stone.

He picked it up, noted the number, and went to his private house for luncheon.

His wife said that the butcher had sent in his bill for $\pounds 5$,

and, as the only money he had was the note he had found, he gave it to her and she paid the butcher.

The butcher paid it to a farmer in buying a calf,

the farmer paid it to a merchant

who in turn paid it to a laundry-woman,

and she, remembering that she owed the bank $\pounds 5$, went there and paid the note.

The banker recognised the note as the one he had found,

and by that time it had paid $\pounds 25$ worth of debts.

On careful examination he discovered that the note was counterfeit.

Now, what was lost in the whole transaction, and by whom?

$35$ - The Reapers' Puzzle

Three men were to receive $90 \shillings$ for harvesting a field, conditionally upon the work being done in $5$ days.

Jake could do it alone in $9$ days, but as Ben was not as good a workman they were compelled to engage Bill for $2$ days,

in consequence of which Ben got $3 \shillings 9 \oldpence$ less than he would otherwise have received.

How long would it have taken Ben and Bill together to complete the work?

$36$ - The Flagons of Wine

A quart of Burgundy costs $4 \shillings 9 \oldpence$, but $3 \oldpence$ is returnable on the empty flagon,

so that the Burgundy seems to be worth $4 \shillings 6 \oldpence$

For $12$ of the capsules with which each of the quart flagons is sealed, a free flagon of the same value is obtained.

What is the value of a single capsule?

Obviously a twelfth of $4 \shillings 6 \oldpence$ which is $4 \tfrac 1 2 \oldpence$

But the free flagon also has a capsule worth $4 \tfrac 1 2 \oldpence$, so that this full flagon appears to be worth $4 \shillings 10 \tfrac 1 2 \oldpence$,

which makes the capsule worth a twelfth of $4 \shillings 10 \tfrac 1 2 \oldpence$, or $4 \tfrac 7 8 \oldpence$,

and so on ad infinitum, with an ever-increasing value.

Where is the fallacy, and what is the real worth of a capsule?

$37$ - A Wages Paradox

"I want a rise, sir," said the office-boy.

"That's nonsense," said the employer.

"If I give you a rise you will really be getting less wages per week than you are getting now."

The boy pondered over this, but was unable to see how such a thing could happen.

Can you explain it?