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

Henry Ernest Dudeney: Modern Puzzles: Arithmetical and Algebraical Problems

$1$ - Concerning a Cheque

A man went into a bank to cash a cheque.

In handing over the money the cashier, by mistake, gave him pounds for shillings and shillings for pounds.

He pocketed the money without examining it, and spent half a crown on his way home, when he found that he possessed exactly twice the amount of the cheque.

He had no money in his pocket before going to the bank, and it is an interesting puzzle to find out what was the exact amount of that cheque.

$2$ - Pocket-money

I went down the street with a certain amount of money in my pocket,

and when I returned home I discovered that I had spent just half of it,

and that I now had just as many shillings as I previously had pounds,

and half as many pounds as I then had shillings.

How much money had I spent?

$3$ - Dollars and Cents

An American correspondent tells me that a man went into a store and spent one-half of the money that was in his pocket.

When he came out he found that he had just as many cents as he had dollars when he went in

and half as many dollars as he had cents when he went in.

How much money did he have on him when he entered?

$4$ - Loose Cash

What is the largest sum of money -- all in current silver coins and no four-shilling piece -- that I could have in my pocket without being able to give change for half a sovereign?

$5$ - Doubling the Value

It is a curious fact that if you double $\pounds 6 \ 13 \shillings$, you get $\pounds 13 \ 6 \shillings$, which is merely changing the shillings and the pounds.

Can you find another sum of money that has the same peculiarity that, when multiplied by any number you may choose to select, will merely exchange the shillings and the pounds?

There is only one other multiplier and sum of money, besides the case shown, that will work.

What is it?

$6$ - Generous Gifts

A generous man set aside a certain sum of money for equal distribution weekly to the needy of his acquaintance.

One day he remarked:

"If there are five fewer applicants next week, you will each receive $2$ shillings more."

Unfortunately, instead of there being fewer there were actually four more persons applying for the gift.

"This means," he pointed out, "that you will each receive one shilling less."

Now, how much did each person receive at that last distribution?

$7$ - Selling Eggs

A woman took a certain number of eggs to market and sold some of them.

The next day, through the industry of her hens, the number left over had been doubled, and she sold the same number as the previous day.

On the third day the new remainder was trebled, and she sold the same number as before.

On the fourth day the remainder was quadrupled, and her sales the same as before.

On the fifth day what had been left over were quintupled, yet she sold exactly the same as on all the previous occasions, and so disposed of her entire stock.

What is the smallest number of eggs she could have taken to market the first day, and how many did she sell daily?

$8$ - Buying Buns

Buns were being sold at three prices:

one a penny,

two a penny,

and three a penny.

Some children (there were as many boys as girls) were given sevenpence to spend on these buns, each receiving exactly alike.

How many buns did each receive?

Of course no buns were divided.

$9$ - Fractional Value

What part of threepence is one-third of twopence?

$10$ - Unrewarded Labour

A man persuaded Weary Willie, with some difficulty, to try to work on a job for $30$ days at $8$ shillings a day,

on the condition that he would forfeit $10$ shillings a day for every day that he idled.

At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labour.

Now, can you tell me just how many days' work he put in, and on how many days he idled?

$11$ - The Perplexed Banker

A man went into a bank with $1000$ sovereigns and $10$ bags.

He said,

"Place this money, please, in the bags in such a way that if I call and ask for a certain number of sovereigns

you can hand me over one or more bags, giving me the exact amount called for without opening any of the bags."

How was it to be done?

We are, of course, only concerned with a single application,

but he may ask for any exact number of pounds from $\pounds 1$ to $\pounds 1000$.

$12$ - A Weird Game

Seven men engaged in play.

Whenever a player won a game he doubled the money of each of the other players.

That is, he gave each player just as much money as each had in his pocket.

They played $7$ games and, strange to say, each won a game in turn in the order of their names,

which began with the letters $\text A$, $\text B$, $\text C$, $\text D$, $\text E$, $\text F$, and $\text G$.

When they had finished it was found that each man had exactly $2$ shillings and $8$ pence in his pocket.

How much had each man had in his pocket before play?

$13$ - Find the Coins

Three men, Abel, Best and Crewe, possessed money, all in silver coins.

Abel had one coin fewer than Best and one more than Crewe.

Abel gave Best and Crewe as much money as they already had,

then Best gave Abel and Crewe the same amount of money as they they held,

and finally Crewe gave Abel and Best as much money as they then had.

Each man then held exactly $10$ shillings.

To find what amount each man started with is not difficult.

But the sting of the puzzle is in the tail.

Each man held exactly the same coins (the fewest possible) amounting to $10$ shillings.

What were the coins and how were they originally distributed?

$14$ - An Easy Settlement

Three men, Andrews, Baker and Carey, sat down to play at some game.

When they put their money on the table it was found that they each possessed $2$ coins only, making altogether $\pounds 1 \ 4 \shillings 6 \oldpence$

At the end of play Andrews had lost $5$ shillings and Carey had lost sixpence, and they all squared up by simply exchanging the coins.

What were the exact coins that each held on rising from the table?

$15$ - Sawing Logs

"Your charge," said Mr. Grigsby, "was $30$ shillings for sawing up $3$ cords of wood made up of logs $3$ feet long,

each log to be cut into pieces $1$ foot in length."

"That is so," the man replied.

"Well, here are $4$ cords of logs, all of the same thickness as before,

only they are in $6$-feet lengths, instead of $3$ feet.

What will your charge be for cutting them all up into similar $1$-foot lengths?"

It is curious that they could not at once agree as to the fair price for the job.

What does the reader think the charge ought to be?

$16$ - Digging a Ditch

Here is a curious question that is more perplexing than it looks at first sight.

Abraham, an infirm old man, undertook to dig a ditch for $2$ pounds.

He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities.

Abraham could dig as fast as Benjamin could shovel out the dirt,

and Benjamin could dig four times as fast as Abraham could do the shovelling.

How should they divide the money?

Of course, we must assume their relative abilities for work to be the same in digging or shovelling.

$17$ - Name their Wives

A man left a legacy of $\pounds 1000$ to $3$ relatives and their wives.

The wives received together $\pounds 396$.

Jane received $\pounds 10$ more than Catherine,

and Mary received $\pounds 10$ more than Jane.

John Smith was given just as much as his wife,

Henry Snooks got half as much again as his wife,

and Tom Crowe received twice as much as his wife.

What was the Christian name of each man's wife?

$18$ - A Curious Paradox

A man went into a shop to pay a little bill that he owed.

On placing the money on the counter he found that he had not quite sufficient,

owing to a small purchase that he had thoughtlessly made on the way.

"I am so sorry," he said, "but you see I am a little short.

"Oh, that is all right," replied the tradesman, after looking at the money, "it won't make any difference to me."

"My good man!" exclaimed the customer ...

... etc. etc. ...

"... But really it will not affect my pocket in the slightest."

Can you explain the mystery?

It may come to you in a flash.

The tradesman was certainly correct.

$19$ - Market Transactions

A farmer goes to market and buys $100$ animals at a total cost of $\pounds 100$.

The price of cows being $\pounds 5$ each,

sheep $\pounds 1$ each,

and rabbits $1 \shillings$ each,

how many of each kind does he buy?

$20$ - The Seven Applewomen

Seven applewomen,

possessing respectively $20$, $40$, $60$, $80$, $100$, $120$, and $140$ apples,

went to market and sold all their apples at the same price,

and each received the same sum of money.

What was the price?