Henry Ernest Dudeney/Puzzles and Curious Problems/Unclassified Problems

Henry Ernest Dudeney: Puzzles and Curious Problems: Unclassified Problems

$320$ - An Awkward Time

When I told someone the other morning that I had to catch the $12:50$ train, he told me it was a very awkward time for a train to start.

I asked him to explain why.

Can you guess his answer?

$321$ - Cryptic Addition

Can you prove that the following addition sum is correct?

$322$ - The New Gun

An inventor undertook that a new gun which he had manufactured, which when once loaded,

would fire fifteen shots at the rate of a shot a minute.

A series of tests were made, and the gun certainly fired fifteen shots in a quarter of an hour.

However, the Government refused to buy the gun, on the grounds that it did not do the job as advertised.

Why?

$323$ - Cats and Mice

A number of cats (more than one) killed between them $999 \, 919$ mice, and every cat killed an equal number of mice (more than one).

Each cat killed more mice than there were cats.

How many cats were there?

$324$ - The Two Snakes

Suppose two snakes started swallowing one another simultaneously,

each getting the tail of the other in its mouth,

so that the circle formed by the snakes becomes smaller and smaller.

What will eventually happen?

$325$ - The Price of a Garden

A neighbour told you he was offered a triangular piece of ground for a garden.

Its sides were $55$ yards, $62$ yards and $117$ yards.

The price was $10$ shillings per square yard.

What will its cost be?

$326$ - Strange Though True

There is a district in Sussex where any healthy horse can travel, quite regularly, $30$ miles per day,

yet while its legs on one side travel $30$ miles, the legs on its other side travel $31$ miles.

The horse, apparently, does not seem to mind this.

How can this be?

$327$ - Two Paradoxes

$(1): \quad$ Imagine a man going to the North Pole.

The points of the compass are, as everyone knows:

$\qquad \qquad \qquad \begin{array} {ccc} & \text N & \\ \text W & & \text E \\ & \text S & \\ \end{array}$

He reaches the pole and, having passed over it, must turn about to look North.

East is now on his left-hand side, West on his right-hand side, and the points of the compass therefore:

$\qquad \qquad \qquad \begin{array} {ccc} & \text N & \\ \text E & & \text W \\ & \text S & \\ \end{array}$

which is absurd.

What is the explanation?

$(2): \quad$ When you look in the mirror, you are turned right round, so that right is left and left is right,

and yet top is not bottom and bottom is not top.

If it reverses sideways, why does it not reverse lengthways?

Why are you not shown standing on your head?

$328$ - Choosing a Site

A man bought an estate enclosed by three straight roads forming an equilateral triangle.

He wished to build a house somewhere on the estate so that if he should have a straight drive from the front to each of the three roads,

he might be put to least expense.

Where should be build the house?

$329$ - The Four Pennies

Take four pennies and arrange them on the table without the assistance of another coin or any means of measurement,

so that when a fifth penny is produced it may be placed in exact contact with each of the four (without moving them)

in the manner shown in the diagram.

The shaded circle represents the fifth penny.

How should you proceed?

$330$ - The Encircled Triangles

Draw the design of circle and triangles in as few continuous strokes as possible.

You may go over a line twice if you wish to do so, and begin and end wherever you like.

How should you proceed?

$331$ - The Siamese Serpent

Draw as much of the serpent as possible using one continuous line,

without taking the pencil off the paper or going over the same line twice.

$332$ - A Bunch of Grapes

Here is a rough conventionalized sketch of a bunch of grapes.

The puzzle is to make a copy of it with one continuous stroke of the pencil,

never lifting the pencil from the paper,

nor going over a line twice throughout.

$333$ - A Hopscotch Puzzle

We saw some boys playing hopscotch, and wondered whether the figure marked on the ground could be drawn in one continuous stroke.

Can the reader draw it without taking the pencil off the paper or going over the same line twice?

$334$ - A Little Match Trick

We pulled open a box of matches the other day, and showed some friends that there were only about $12$ matches in it.

When opened at that end no heads were visible.

The heads were all at the other end of the box.

We told them after they had closed the box in front of them that we would give it a shake, and on reopening,

they would find a match turned round with its head visible.

They afterwards examined it to see that the matches were all sound.

$335$ - Three Times the Size

Lay out $20$ matches in the way shown in the diagram.

You will see that the two groups of $6$ and $14$ matches form two enclosures, so that one space is exactly $3$ times as large as the other.

Now transfer one match from the larger to the smaller group, and with the $7$ and $13$ enclose two spaces again, one exactly $3$ times as large as the other.

Twelve of the matches must remain unmoved from their present positions --

and there must be no duplicated matches or loose ends.

The dotted lines are just there to indicate the respective areas.

$336$ - A Six-Sided Figure

Here are $6$ matches arranged to form a regular hexagon.

Can you take $3$ more matches and so arrange the $9$ as to show another regular $6$-sided figure?

$337$ - Twenty-Six Matches

Make a rough square diagram, like the one shown, where the side of each square is the length of a match,

and put the stars and crosses in their given positions.

It is required to put $26$ matches along the lines so as to enclose $2$ parts of exactly the same size and shape,

one part enclosing two stars, and the other part enclosing two crosses.

In the example given, each part is correctly the same size and shape, and each part contains either two stars or two crosses,

but unfortunately only $20$ matches have been used.

$338$ - The Three Matches

Can you place $3$ matches on the table, and support the matchbox on them,

without allowing the heads of the matches to touch the table, to touch one another, or to touch the box?

$339$ - Equilateral Triangles

Place $16$ matches, as shown, to form $8$ equilateral triangles.

Now take away $4$ matches so as to leave $4$ equal triangles.

No superfluous matches or loose ends to be left.

$340$ - Squares with Matches

Arrange $12$ matches on the table, as shown in the diagram.

Now it is required to remove $6$ of these matches and replace them so as to form $5$ squares.

Of course $6$ matches must remain unmoved, and there must be no duplicated matches or loose ends.

$341$ - Hexagon to Diamonds

Arrange $6$ matches form a hexagon, as here shown.

Now, by moving only $2$ matches and adding $1$ more, can you form two diamonds?

$342$ - A Wily Puzzle

A life prisoner appealed to the king for pardon.

Not being ready to favour the appeal, the king proposed a pardon on condition that the prisoner should start at cell $A$

and go in and out of each cell of the prison, coming back to the cell $A$ without going into any cell twice.

$343$ - Tom Tiddler's Ground

I am on Tom Tiddler's ground picking up gold and silver.

Here we have a piece of land marked off with $36$ circular plots,

on each of which is deposited a bag containing as many sovereigns as the figures indicate in the diagram.

I am allowed to pick up as many bags of gold as I like,

provided I do not take two lying on the same line.

What is the greatest amount of money I can secure?

$344$ - Coin and Hole

We have before us a specimen of every coin which was current in Britain in $1930$.

And we have a sheet of paper with a circular hole cut in it $\tfrac 3 4$ of an inch in diameter.

What is the largest coin I can pass through that hole without tearing the paper?

$345$ - The Egg Cabinet

A man has a cabinet for holding birds' eggs.

There are $12$ drawers, and all -- except the first drawer, which holds the catalogue -- are divided into cells by intersecting wooden strips,

running the entire length or width of a drawer.

The number of cells in any drawer is greater than that of the drawer above.

The bottom drawer, No. $12$, has $12$ times as many cells as strips,

No. $11$ has $11$ times as many cells as strips, and so on.

Can you show how the drawers were divided -- how many cells and strips in each drawer?

Give the smallest possible number in each case.

$346$ - A Leap Year Puzzle

The month of February in $1928$ contained five Wednesdays.

There is, of course, nothing remarkable in this fact, but it will be found interesting to discover

when was the last year and when will be the next year that had, and that will have, $5$ Wednesdays in February.

$347$ - The Iron Chain

Two pieces of iron chain were picked up on the battlefield.

What purpose they had originally served is not certain, and does not immediately concern us.

They were formed of circular iron links (all of the same size) out of metal half an inch thick.

One piece of chain was exactly $3$ feet long, and the other $22$ inches in length.

Now, as one piece contained exactly six links more than the other, how many links were there in each piece of chain?

$348$ - Blowing Out the Candle

Candles were lighted on Colonel Crackham's breakfast-table one foggy morning.

When the fog lifted, the Colonel rolled a sheet of paper into the form of a hollow cone, like a megaphone.

He then challenged his young friends to use it in blowing out the candles.

They failed, until he showed them the trick.

Of course, you blow through the small end.

$349$ - Releasing the Stick

It is simply a loop of string passed through one end of a stick as here shown, but not long enough to pass round the other end.

The puzzle is to suspend it in the manner shown from the top hole of a man's coat, and then get it free again.

$350$ - The Keys and Ring

Colonel Crackham the other day produced a ring and two keys, as here shown,

cut out of a solid piece of cardboard, without a break or join anywhere.

$351$ - The Entangled Scissors

If you start on the loop at the bottom, the string can readily be got into position.

The puzzle is, of course, to let someone hold the two ends of the string until you disengage the scissors.

A good length of string should be used to give you free play.

$352$ - Locating the Coins

Said Dora to her brother:

"Put a shilling in one of your pockets and a penny in the pocket in the opposite side.

Now the shilling represents $12$ and the penny $1$.

Triple the coin in your right pocket, and double that in your left pocket.

Add these products together and tell me whether the result is odd or even."

He said the result was even, and she immediately told him that the shilling was in the right pocket and the penny in the left one.

Every time he tried it she told him correctly how the coins were located.

How did she do it?

$353$ - The Three Sugar Basins

Three basins each contain the same number of lumps of sugar,

and nine cups are empty.

If we transfer to each cup one-eighteenth of the number of lumps that each basin contains,

we then find that each basin holds $12$ more lumps than each of the cups.

How many lumps are there in each basin before they are removed?

$354$ - The Wheels of the Car

"You see, sir," said the motor-car salesman, "at present the fore-wheel of the car I am selling you makes four revolutions more than the hind-wheel in going $120$ yards;

but if you have the circumference of each wheel reduced by $3$ feet, it would make as many as six revolutions more than the hind-wheel in the same distance."

Why the buyer wished that the difference in the number of revolutions between the two wheels should not be increased does not concern us.

The puzzle is to discover the circumference of each wheel in the first case.

$355$ - The Seven Children

Four boys and three girls are seated in a row at random.

What are the chances that the two children at the end of each row will be girls?

$356$ - A Rail Problem

There is a garden railing similar to our design.

In each division between two uprights there is an equal number of ornamental rails,

and a rail is divided in halves and a portion stuck on each side of every upright,

except that the uprights at the end have not been given half rails.

Idly counting the rails from one end to another, we found that there were $1223$ rails, counting two halves as one rail.

We also noticed that the number of those divisions was five more than twice the number of whole rails in a division.

How many rails were there in each division?

$357$ - The Wheel Puzzle

Place the numbers $1$ to $19$ in the $19$ circles,

so that wherever there are three in a straight line they shall add up to $30$.

$358$ - Simple Addition

Can you show that four added to six will make eleven?

$359$ - Queer Arithmetic

Can you take away seven-tenths from five so that exactly four remains?

$360$ - Fort Garrisons

Here we have a system of fortifications.

It will be seen that there are ten forts, connected by lines of outworks,

and the numbers represent the strength of the small garrisons.

The General wants to dispose these garrisons afresh so that there shall be $100$ men in every one of the five lines of four forts.

The garrison must be moved bodily -- that is to say, you are not allowed to break them up into other numbers.

$361$ - Constellation Puzzle

The arrangement of stars in the diagram is known as "The British Constellation".

It is not given in any star map or books, and it is very difficult to find on the clearest night for the simple reason that it is not visible.

The $21$ stars form seven lines with $5$ stars in every line.

Can you rearrange these $21$ stars so that they form $11$ straight lines with $5$ stars in every line?

$362$ - Intelligence Tests

An English officer fell asleep in church during a sermon.

He was dreaming that the executioner was approaching him to cut off his head,

and just as the sword was descending on the officer's unhappy neck

his wife lightly touched her husband on the back of his neck with her fan to awaken him.

The shock was too great, and the officer fell forward dead.

Now, there is something wrong with this.

What is it?

Another such question goes along these lines:

If we sell apples by the cubic inch,

how can we really find the exact number of cubic inches in, say, a dozen dozen apples?

$363$ - At the Mountain Top

"When I was in Italy I was taken to the top of a mountain

and shown that a mug would hold less liquor at the top of the mountain than in the valley beneath.

Can you tell me," asked Professor Rackbrane, "what mountain this might be that has so strange a property?"

$364$ - Cupid's Arithmetic

Dora Crackham one morning produced a slip of paper bearing the jumble of figures shown in our diagram.

She said that a young mathematician had this poser presented to him by his betrothed when she was in a playful mood.

"What am I to do with it?" asked George.

"Just interpret its meaning," she replied. "If it is properly regarded it should not be difficult to decipher."

$365$ - Tangrams

In the diagram the square is shown cut into the $7$ pieces.

If you mark the point $B$, midway between $A$ and $C$, on one side of a square of any size,

and $D$, midway between $C$ and $E$, on an adjoining side, the direction of the cuts is obvious.