nyuuzyou/wikis huggingface dataset:
Henry Ernest Dudeney/Puzzles and Curious Problems/324 - The Two Snakes/Solution

== by : $324$ ==
;The Two Snakes
== Solution ==
 is vague:
:We cannot say how much of each snake must be swallowed before a vital organ is sufficiently affected to cause death.
Each snake, of course, has a stomach which is a fraction of its actual length, and of a limited size, and when one snake has swallowed enough of the other to fill its stomach, there it will stop.
It is of course theoretically possible, for snakes which have large enough stomachs, for part of its own tail to be inside its own stomach.
In the extreme, one supposes there will be a tight hard ball of many layers of extremely full snakes, both digesting each other torpidly, until both are dead.
Unless, of course, a snake's skin is proof against the digestive juices of the stomach of the other, in which case one also presumes they will eventually regurgitate each other.
 continues:
:But we can say what will not happen -- that the snakes will go on swallowing one another until both disappear altogether!
:But where it will really end is impossible to say.
The author of this page has resolutely refused to google it.
== Sources ==
* : Solutions: $324$. -- The Two Snakes
* : Answers: $525$. The Two Snakes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/325 - The Price of a Garden

== by : $325$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $325$. -- The Price of a Garden
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $283$. The Price of a Garden
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/325 - The Price of a Garden/Solution

== by : $325$ ==
;The Price of a Garden
== Solution ==
Nothing.
== Proof ==
We have that:
:$55 + 62 = 117$
and so a triangle with those sides will have zero area.
Hence and so.
== Sources ==
* : Solutions: $325$. -- The Price of a Garden
* : Answers: $283$. The Price of a Garden
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/326 - Strange Though True

== by : $326$ ==
;Strange Though True
:There is a district in 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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $326$. -- Strange Though True
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/326 - Strange Though True/Solution

== by : $326$ ==
;Strange Though True
== Solution ==
It does not have to be , of course.
It can be anywhere the horse is working a machine, say a chaff-cutter, in which it is constrained to walking round and round in a circle of tight enough radius.''
== Sources ==
* : Solutions: $326$. -- Strange Though True
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/327 - Two Paradoxes

== by : $327$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $327$. -- Two Paradoxes
* : Unclassified Puzzles: $526$. Two Paradoxes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/327 - Two Paradoxes/Solution

== by : $327$ ==
;Two Paradoxes
== Solution ==
:$(1): \quad$ As you go over the pole, and are facing South, so also are West and East changed over.
:::So, without turning round to face North, West is already on your right and East on your left.
:::So when you turn round to face North, West is on your left and East on your right, and all is well with the world.
:$(2): \quad$ When you look in a mirror, it is not left and right which are exchanged, but front and back.
== Historical Note ==
== Sources ==
* : Solutions: $327$. -- Two Paradoxes
* : Answers: $526$. Two Paradoxes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/328 - Choosing a Site

== by : $328$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $328$. -- Choosing a Site
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $284$. Choosing a Site
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/328 - Choosing a Site/Solution

== by : $328$ ==
;Choosing a Site
== Solution ==
Anywhere he likes.
== Proof ==
In 's words:
:This was a little jest.
Let perpendiculars be drawn to the sides of an equilateral triangle from any point within it.
Then from Viviani's Theorem, the sum of their lengths is equal to the height of that equilateral triangle.
So, from whatever point you choose inside this equilateral triangle, the sum of those lengths is the same.
== Sources ==
* : Solutions: $328$. -- Choosing a Site
* : Answers: $284$. Choosing a Site
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/329 - The Four Pennies

== by : $329$ ==
;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?
=== Click here for solution ===
== Also see ==
* by : $213$ - The Six Pennies
== Sources ==
* : Unclassified Problems: $329$. -- The Four Pennies
* : Geometrical Problems: Moving Counter Puzzles: $382$. The Four Pennies
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/329 - The Four Pennies/Solution

== by : $329$ ==
;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?
== Solution ==
Arrange the pennies as follows.
:
Note they have been labeled from $1$ to $4$.
Move penny no. $1$ to touch $2$ and $4$:
:
Move penny no. $4$ to touch $2$ and $3$:
:
== Sources ==
* : Solutions: $329$. -- The Four Pennies
* : Answers: $382$. The Four Pennies
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/32 - Apple Transactions

== by : $32$ ==
;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 $100$?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $32$. -- Apple Transactions
* : Arithmetical and Algebraical Problems: Money Puzzles: $29$. Apple Transactions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/32 - Apple Transactions/Solution

== by : $32$ ==
;Apple Transactions
== Solution ==
:$8 \shillings$
== Proof ==
Let $p$ be the price per apple in pence.
Let $n$ be the number of apples that were bought for $10 \shillings$, that is, $120 \oldpence$
Then we have:
Only the positive root is appropriate here.
Hence:
:$p = \dfrac {96} {100}$
That is, the price for $100$ apples is $96 \oldpence$, which works out as $\dfrac {96} {12} = 8 \shillings$
== Sources ==
* : Solutions: $32$. -- Apple Transactions
* : Answers: $29$. Apple Transactions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/330 - The Encircled Triangles

== by : $330$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $330$. -- The Encircled Triangles
* : Combinatorial & Topological Problems: Route & Network Puzzles: $430$. The Encircled Triangles
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/330 - The Encircled Triangles/Solution

== by : $330$ ==
;The Encircled Triangles
== Solution ==
It can be done in $14$ strokes.
Refer to the below diagram.
:
Draw the straight lines $ABCDEFAGHI$ which is $9$ strokes.
Note we have visited $A$ twice during this excursion.
Draw one stroke round the circle and back to $I$ again, which is one stroke, making $10$ so far.
Draw $IJKLJ$ which is $4$ more strokes, making $14$ in all.
Note that we have gone over the short segment $AJ$ twice, while the rest of the diagram is traversed only once.
The question is flawed, in that it does not say you must perform this task without lifting the pencil from the paper.
However, from a view of the answer, it is clear that is what is meant.
== Sources ==
* : Solutions: $330$. -- The Encircled Triangles
* : Answers: $430$. The Encircled Triangles
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/331 - The Siamese Serpent

== by : $331$ ==
;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.
:
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $331$. -- The Siamese Serpent
* : Combinatorial & Topological Problems: Route & Network Puzzles: $431$. The Siamese Serpent
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/331 - The Siamese Serpent/Solution

== by : $331$ ==
;The Siamese Serpent
== Solution ==
:The drawing cannot be executed under the conditions in fewer than $13$ lines.
:The longest of these lines is one which starts at $A$ and ends at $B$ in the diagram.
:
:The dotted lines are the ones which have been omitted.
:Thus, the unbroken line from $D$ to $C$ is longer than the broken one, so we take the former.
:Again, we get a little more of the drawing by taking the tongue rather than the mouth,
::but the part of the tongue ending in a single line has to be omitted.
== Sources ==
* : Solutions: $331$. -- The Siamese Serpent
* : Answers: $431$. The Siamese Serpent
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/332 - A Bunch of Grapes

== by : $332$ ==
;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.
:
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $332$. -- A Bunch of Grapes
* : Combinatorial & Topological Problems: Route & Network Puzzles: $432$. A Bunch of Grapes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/332 - A Bunch of Grapes/Solution

== by : $332$ ==
;A Bunch of Grapes
== Solution ==
:There are various routes possible, and the diagram shows one of them.
:
:It is absolutely necessary that you begin at $A$ and end at $B$, or the reverse.
== Sources ==
* : Solutions: $332$. -- A Bunch of Grapes
* : Answers: $432$. A Bunch of Grapes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/333 - A Hopscotch Puzzle

== by : $333$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $333$. -- A Hopscotch Puzzle
* : Combinatorial & Topological Problems: Route & Network Puzzles: $433$. A Hopscotch Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/333 - A Hopscotch Puzzle/Solution

== by : $333$ ==
;A Hopscotch Puzzle
== Solution ==
:It is necessary to start at $A$ and end at $B$, or start at $B$ and end at $A$, otherwise it can't be done.
:
== Sources ==
* : Solutions: $333$. -- A Hopscotch Puzzle
* : Answers: $433$. A Hopscotch Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/334 - A Little Match Trick

== by : $334$ ==
;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.
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $334$. -- A Little Match Trick
* : Match Puzzles: $501$. A Match Trick
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/334 - A Little Match Trick/Solution

== by : $334$ ==
;A Little Match Trick
== Solution ==
:Hide the match inside in the manner shown by the dotted lines in the diagram,
::so the head is just over the edge of the tray of the box.
:
:In closing the box you push this extra match forward with your thumbnail and it falls into place.
:The fact that there are now more matches in the box than when you first showed it does not matter, because nobody actually counts the matches.
== Sources ==
* : Solutions: $334$. -- A Little Match Trick
* : Answers: $501$. A Match Trick
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/335 - Three Times the Size

== by : $335$ ==
;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.
=== Click here for solution ===
== Also see ==
* $211$ - The Twenty Matches, in the same collection
== Sources ==
* : Unclassified Problems: $335$. -- Three Times the Size
* : Match Puzzles: $502$. Three Times the Size
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/335 - Three Times the Size/Solution

== by : $335$ ==
;Three Times the Size
== Solution ==
:
== Also see ==
* $211$ - The Twenty Matches, in the same collection
== Sources ==
* : Solutions: $335$. -- Three Times the Size
* : Answers: $502$. Three Times the Size
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/336 - A Six-Sided Figure

== by : $336$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $336$. -- A Six-Sided Figure
* : Match Puzzles: $503$. A Six-Sided Figure
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/336 - A Six-Sided Figure/Solution

== by : $336$ ==
;A Six-Sided Figure
== Solution ==
:
Yes okay, we cheated.
This is in fact a perspective representation of a cube.
The six "sides" are of course its faces.
== Sources ==
* : Solutions: $336$. -- A Six-Sided Figure
* : Answers: $503$. A Six-Sided Figure
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/337 - Twenty-Six Matches

== by : $337$ ==
;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.
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $337$. -- Twenty-Six Matches
* : Match Puzzles: $504$. Twenty-Six Matches
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/338 - The Three Matches

== by : $338$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $338$. -- The Three Matches
* : Match Puzzles: $505$. The Three Matches
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/338 - The Three Matches/Solution

== by : $338$ ==
;The Three Matches
== Solution ==
:Arrange the three matches as shown in the diagram, and stand the box on end in the centre.
:
== Sources ==
* : Solutions: $338$. -- The Three Matches
* : Answers: $505$. The Three Matches
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/339 - Equilateral Triangles

== by : $339$ ==
;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.
:
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $339$. -- Equilateral Triangles
* : Match Puzzles: $506$. Equilateral Triangles
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/339 - Equilateral Triangles/Solution

== by : $339$ ==
;Equilateral Triangles
== Solution ==
:
The dotted lines indicate the matches which are to be removed.
== Sources ==
* : Solutions: $339$. -- Equilateral Triangles
* : Answers: $506$. Equilateral Triangles
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/33 - Prosperous Business

== by : $33$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $33$. -- Prosperous Business
* : Arithmetical and Algebraical Problems: Money Puzzles: $30$. Prosperous Business
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/33 - Prosperous Business/Solution

== by : $33$ ==
;Prosperous Business
== Solution ==
:$\pounds 22 \, 781, 5 \shillings$
== Proof ==
Let $T$ be the total required.
We have:
:$T = 2000 \times \paren {\dfrac 3 2}^6$
which evaluates to:
:$T = 22 \, 781 \cdotp 25$
== Sources ==
* : Solutions: $33$. -- Prosperous Business
* : Answers: $30$. Prosperous Business
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/340 - Squares with Matches

== by : $340$ ==
;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.
:
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $340$. -- Squares with Matches
* : Match Puzzles: $507$. Squares with Matches
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/340 - Squares with Matches/Solution

== by : $340$ ==
;Squares with Matches
== Solution ==
:
The dotted lines indicate where the $6$ matches were moved from.
The red lines indicate where the $6$ matches were moved to.
== Sources ==
* : Solutions: $340$. -- Squares with Matches
* : Answers: $507$. Squares with Matches
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/341 - Hexagon to Diamonds

== by : $341$ ==
;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?
:
=== Click here for solution ===
== Sources ==
* : Unclassified Problems: $341$. -- Hexagon to Diamonds
* : Match Puzzles: $508$. Hexagon to Diamonds
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/341 - Hexagon to Diamonds/Solution

== by : $341$ ==
;Hexagon to Diamonds
== Solution ==
The dotted lines show where the matches were moved from.
The red lines show where they were moved to, and where the new one was added.
:
== Sources ==
* : Solutions: $341$. -- Hexagon to Diamonds
* : Answers: $508$. Hexagon to Diamonds
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions