nyuuzyou/wikis huggingface dataset:
Henry Ernest Dudeney/Modern Puzzles/108 - Hexagon to Square/Solution

== by : $108$ ==
;Hexagon to Square
:Can you cut a regular hexagon into $5$ pieces that will fit together to form a square?
== Solution ==
:
Cut the hexagon in half along a diagonal and place the two parts together to form the parallelogram $ABCD$.
Construct $CF$ perpendicular to $DC$.
Produce $DC$ to $E$ where $CE = CF$.
Construct the semicircle $DHE$, whose center will be at $G$.
Produce $CF$ to $H$.
We have that $CH^2 = DC \cdot CE$.
We have that $DC \cdot CE$ is the area of the parallelogram $ABCD$, and therefore the original hexagon.
Hence a square whose side is $CH$ will have the same area as that hexagon.
Construct the semicircle $DJC$, whose center will be at $K$.
Construct the arc $HJ$ whose center is at $C$.
Draw $CJ$ and $DJ$.
Construct $LJ = CJ$ and the follows.
The rest explains itself.
== Historical Note ==
== Sources ==
* : Solutions: $108$. -- Hexagon to Square
* : Answers: $331$. Hexagon to Square
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/109 - Squaring a Star

== by : $109$ ==
;Squaring a Star
:This six-pointed star can be cut into as few as five pieces that will fit together to form a perfect square.
:To perform the feat in $7$ pieces is quite easy,
::but to do it in $5$ is more difficult.
:
:The dotted lines are there to show the true shape of the star, which is made of $12$ equilateral triangles.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $109$. -- Squaring a Star
* : Geometrical Problems: Dissection Puzzles: $332$. Squaring a Star
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/109 - Squaring a Star/Solution

== by : $109$ ==
;Squaring a Star
== Solution ==
:
Find the side of the equal square by calculating the mean proportional between $AB$ and $BC$.
Make $BD$ equal to such.
Drop a perpendicular from $A$ to $BD$ at $E$, and $AE$ will equal $BD$.
The rest follows straightforwardly.
== Historical Note ==
== Sources ==
* : Solutions: $109$. -- Squaring a Star
* : Answers: $332$. -- Squaring a Star
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/109 - Squaring a Star/Solution/Historical Note

== by : $109$ ==
 attributes this result to .
 erroneously references the dissections illustrated by as Figures $3.3$ and $3.4$ in his , but these appear to be of the regular hexagon to the square.
== Sources ==
* : Solutions: $109$. -- Squaring a Star
* : Answers: $332$. -- Squaring a Star
Category:Historical Notes
Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour

== by : $10$ ==
;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?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $10$. -- Unrewarded Labour
* : Arithmetical and Algebraical Problems: Money Puzzles: $6$. Unrewarded Labour
Category:Henry Ernest Dudeney/Modern Puzzles
Category:Part-Time Carpenter
Henry Ernest Dudeney/Modern Puzzles/10 - Unrewarded Labour/Solution

== by : $10$ ==
;Unrewarded Labour
== Solution ==
$16 \tfrac 2 3$ days.
== Proof ==
Let $d$ be the number of days Willie worked.
We have:
== Sources ==
* : Solutions: $10$. -- Unrewarded Labour
* : Answers: $6$. Unrewarded Labour
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/110 - The Mutilated Cross

== by : $110$ ==
;The Mutilated Cross
:Here is a regular Greek cross from which has been cut a square piece exactly equal to one of the arms of the cross.
:
:The puzzle is to cut what remains into four pieces that will fit together and form a square.
:This is a pleasing but particularly easy cutting out puzzle.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $110$. -- The Mutilated Cross
* : Geometrical Problems: Dissection Puzzles: $333$. The Mutilated Cross
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/110 - The Mutilated Cross/Solution

== by : $110$ ==
;The Mutilated Cross
== Solution ==
:The illustration shows clearly how to cut the mutilated cross into four pieces to form a square.
:
:Just continue each side of the square until you strike a corner, and there you are!
== Sources ==
* : Solutions: $110$. -- The Mutilated Cross
* : Answers: $333$. The Mutilated Cross
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/111 - The Victoria Cross

== by : $111$ ==
;The Victoria Cross
:We have shown elsewhere how innumerable puzzles may be devised on the Greek, St. George, or Red Cross, so familiar to all,
::composed as it is of five equal squares assembled together.
:Let us now do homage to the Maltese or Victoria Cross.
:Cut the cross shown into seven pieces that will fit together and form a perfect square.
:Of course, there must be no trickery or waste of material.
:
:In order that the reader may have no doubt as to the exact proportions of the cross as given, I have inserted the dotted lines.
:As the pieces $A$ and $B$ will fit together to form one of those little squares,
::it is clear that the area of the cross is equal to seventeen such squares.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $111$. -- The Victoria Cross
* : Geometrical Problems: Dissection Puzzles: $334$. The Victoria Cross
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/112 - Squaring the Swastika

== by : $112$ ==
;Squaring the Swastika
:Cut out the swastika and then cut it up into four pieces that will fit together and form a square.
:
:There can be no question as to the proportions of the figure if we regard it as built up of $17$ equal squares.
=== Click here for solution 1 ===
=== Click here for solution 2 ===
=== Click here for solution 3 ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $112$. -- Squaring the Swastika
* : Geometrical Problems: Dissection Puzzles: $335$. Squaring the Swastika
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/112 - Squaring the Swastika/Historical Note

== Historical Note on by : $112$ - Squaring the Swastika ==
In his $1968$ repackaging , references 's symmetrical solution $2$ and solution $3$, published in $1964$.
== Sources ==
* : Answers: $335$. Squaring the Swastika
Category:Historical Notes
Henry Ernest Dudeney/Modern Puzzles/112 - Squaring the Swastika/Solution 1

== by : $112$ ==
;Squaring the Swastika
== Solution ==
:
== Historical Note ==
== Sources ==
* : Solutions: $112$. -- Squaring the Swastika
* : Answers: $335$. Squaring the Swastika
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/113 - The Maltese Cross

== by : $113$ ==
;The Maltese Cross
:Can you cut the star into four pieces and place them inside the frame so as to show a perfect Maltese cross?
:
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $113$. -- The Maltese Cross
* : Geometrical Problems: Dissection Puzzles: $336$. The Maltese Cross
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/113 - The Maltese Cross/Solution

== by : $113$ ==
;The Maltese Cross
== Solution ==
:Cut the star in four pieces across the centre, and place them in the four corners of the frame.
:Then you have a perfect Maltese Cross in white, as indicated.
:
== Sources ==
* : Solutions: $113$. -- The Maltese Cross
* : Answers: $336$. The Maltese Cross
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/114 - The Pirates' Flag

== by : $114$ ==
;The Pirates' Flag
:Here is a flag taken from a band of pirates on the high seas.
:The twelve stripes represented the number of men in the band,
::and when a new man was admitted or dropped out a new stripe was added or one removed, as the case might be.
:Can you discover how the flag should be cut into as few pieces as possible so that they may be put together again and show only ten stripes?
:No part of the material may be wasted, and the flag must retain its oblong shape.
:
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $114$. -- The Pirates' Flag
* : Geometrical Problems: Dissection Puzzles: $337$. The Pirates' Flag
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/114 - The Pirates' Flag/Solution

== by : $114$ ==
;The Pirates' Flag
== Solution ==
:The illustration will show that the flag need only be cut in two pieces -- along the zigzag line.
:If the lower piece is then moved up one step we shall get a flag with the required ten stripes.
:
== Sources ==
* : Solutions: $114$. -- The Pirates' Flag
* : Answers: $337$. The Pirates' Flag
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/115 - The Carpenter's Puzzle

== by : $115$ ==
;The Carpenter's Puzzle
:Here is a well-known puzzle, given in all the old books.
:A ship's carpenter had to stop a hole $12$ inches square,
::and the only piece of wood that was available measured $9 \ \mathrm{in.}$ in breadth by $16 \ \mathrm{in.}$ length.
:How did he cut it into only two pieces that would exactly fit the hole?
:The answer is based on the "step principle", as shown in the diagram.
:
:If you move the piece marked $B$ up one step to the left,
::it will exactly fit on $A$ and form a perfect square measuring $12$ inches on every side.
:This is very simple and obvious.
:But nobody has ever attempted to explain the general law of the thing.
:As a consequence, the notion seems to have got abroad that the method will apply to any rectangle where the proportion of length to breadth is within reasonable limits.
:This is not so, and I have had to expose some bad blunders in the case of published puzzles that were supposed to be solved by an application of this step principle,
::but were really impossible of solution.$^*$
:Let the reader take different measurements, instead of $9 \ \mathrm{in.}$ by $16 \ \mathrm{in.}$,
::and see if he [or she] can find other cases in which this trick will work in two pieces and form a perfect square.
=== Click here for solution ===
== Historical Note ==
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $115$. -- The Carpenter's Puzzle
* : Geometrical Problems: Dissection Puzzles: $338$. The Carpenter's Puzzle
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/115 - The Carpenter's Puzzle/Historical Note

== by : $115$ ==
 points out that , in Problem $150$ in his , catches out in exactly such a blunder.
He does this in , his $1968$ repackaging of 's and .
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $338$. The Carpenter's Puzzle (footnote $^*$)
Category:Historical Notes
Henry Ernest Dudeney/Modern Puzzles/115 - The Carpenter's Puzzle/Solution

== by : $115$ ==
;The Carpenter's Puzzle
== Solution ==
There is only one general situation in which it is possible to dissect a rectangle into two pieces using this specific technique in order to make a square.
That is when the sides of the rectangle are in the proportion of consecutive square numbers.
Thus for a rectangle whose sides are in the ratio $n^2 : \paren {n + 1}^2$, a cut of $n$ steps is used to dissect it into a square whose sides are $n \paren {n + 1}$.
== Proof ==
== Sources ==
* : Solutions: $115$. -- The Carpenter's Puzzle
* : Answers: $338$. The Carpenter's Puzzle
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/116 - The Crescent and the Star

== by : $116$ ==
;The Crescent and the Star
:Here is a little puzzle on the Crescent and the Star.
:Look at the illustration, and see if you can determine which is the larger, the Crescent or the Star.
:If both were cut out of a sheet of solid gold, which would be more valuable?
:
:As it is very difficult to guess by the eye,
::I will state that the outer arc is a semicircle;
::the radius of the inner arc is equal to the straight line $BC$;
:the distance in a straight line from $A$ to $B$ is $12$ units,
:and the point of the star, $D$, contains $3$ square units.
:Now it is quite easy to settle the matter at a glance -- when you know how.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $116$. -- The Crescent and the Star
* : Geometrical Problems: Dissection Puzzles: $339$. The Crescent and the Star
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/116 - The Crescent and the Star/Solution

== by : $116$ ==
;The Crescent and the Star
== Solution ==
They are both the same area: $36$ square units.
== Proof ==
There are $12$ instances of the small equilateral triangle that forms the point $D$.
Hence the area of the star is $12 \times 3 = 36$ square units.
From Lune of Hippocrates, the area of the crescent is equal to the area of the square whose diagonal equals $BC$.
The side of this square is half the distance $AB$, which is $6$.
Hence from Area of Square, the area of the crescent is equal to $6 \times 6$, that is, $36$ square units.
== Sources ==
* : Solutions: $116$. -- The Crescent and the Star
* : Answers: $339$. The Crescent and the Star
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/117 - The Patchwork Quilt

== by : $117$ ==
;The Patchwork Quilt
:Here is a patchwork quilt that was produced by two young ladies for some charitable purpose.
:
:When they came to join their work it was found that each lady had contributed a portion that was exactly the same size and shape.
:It is an amusing puzzle to discover just where these two portions are joined together.
:Can you divide the quilt into two parts, simply by cutting the stitches, so that the portions shall be of the same size and shape?
:You may think you have solved it in a few minutes, but -- wait and see!
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Patchwork Puzzles: $117$. -- The Patchwork Quilt
* : Geometrical Problems: Dissection Puzzles: $340$. The Patchwork Quilt
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/117 - The Patchwork Quilt/Solution

== by : $117$ ==
;The Patchwork Quilt
== Solution ==
:Except for my warning the reader might have supposed that the dark zigzag line from $A$ to $B$ would solve the puzzle.
:But it will not, because the pieces are not of the same size and shape.
:It would be all right if we could go along the dotted line $D$ instead of $C$, but that would mean cutting a piece.
:
:We must cut out all the shaded portion on one piece, which will exactly match the other.
:One portion of the patchwork is drawn in just to guide the eye when comparing with the original.
== Sources ==
* : Solutions: $117$. -- The Patchwork Quilt
* : Answers: $340$. The Patchwork Quilt
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/118 - The Improvised Draughts-Board

== by : $118$ ==
;The Improvised Draughts-Board
:Some Englishmen at the front during the Great War wished to pass a restful hour at a game of draughts.
:They had coins and small stones for the men, but no board.
:However, one of them found a piece of linoleum as shown n the illustration,
::and, as it contained the right number of squares, it was decided to cut it and fit the pieces together to form a board,
::blacking some of the squares afterwards for convenience in playing.
:
:An ingenious Scotsman showed how this could be done by cutting the stuff in two pieces only,
:and it is a really good puzzle to discover how he did it.
:Cut the linoleum along the lines into two pieces that will fit together and form the board, eight by eight.
=== Click here for solution ===
== Linguistic Note ==
== Sources ==
* : Geometrical Problems: Patchwork Puzzles: $118$. -- The Improvised Draughts-Board
* : Geometrical Problems: Dissection Puzzles: $341$. The Improvised Checkerboard
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/118 - The Improvised Draughts-Board/Linguistic Note

== Linguistic Note on Henry Ernest Dudeney's Modern Puzzles: $118$ - The Improvised Draughts-Board ==
Non-British readers may need to know that draughts (pronounced drafts) is what the game is known as in Britain.
Also note that the Great War is what the () was known as before the () surpassed it in horror.
Category:Linguistic Notes
Henry Ernest Dudeney/Modern Puzzles/118 - The Improvised Draughts-Board/Solution

== by : $118$ ==
;The Improvised Draughts-Board
== Solution ==
:
== Linguistic Note ==
== Sources ==
* : Solutions: $118$. -- The Improvised Draughts-Board
* : Answers: $341$. The Improvised Checkerboard
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/119 - Tessellated Pavements

== by : $119$ ==
;Tessellated Pavements
:The reader must often have noticed, in looking at tessellated pavements and elsewhere,
::that a square space had sometimes to be covered with square tiles under such conditions that a certain number of the tiles have to be cut in two parts.
:A familiar example is shown in the illustration, where a square has been formed with ten square tiles.
:
:As ten is not a square number a certain number of tiles must be cut.
:In this case it is six.
:It will be seen that the pieces $1$ and $1$ are cut from one tile, $2$ and $2$ from another, and so on.
:Now, if you had to cover a square space with exactly twenty-nine square tiles of equal size, how would you do it?
:What is the smallest number of tiles that you need cut in two parts?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Patchwork Puzzles: $119$. -- Tessellated Pavements
* : Geometrical Problems: Dissection Puzzles: $342$. Tessellated Pavements
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/119 - Tessellated Pavements/Solution

== by : $119$ ==
;Tessellated Pavements
== Solution ==
:
:The illustration shows how the square space may be covered with twenty-nine square tiles,
::by laying down seventeen whole tiles and cutting each of the remaining twelve tiles in two parts.
:Two parts having the same number form a whole tile.
== Sources ==
* : Solutions: $119$. -- Tessellated Pavements
* : Answers: $342$. Tessellated Pavements
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker

== by : $11$ ==
;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 $\pounds 1000$.
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $11$. -- The Perplexed Banker
* : Arithmetical and Algebraical Problems: Money Puzzles: $7$. The Perplexed Banker
Category:Henry Ernest Dudeney/Modern Puzzles
Category:Binary Notation
Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker/Solution

== by : $11$ ==
;The Perplexed Banker
== Solution ==
For $n = 1$ to $9$, put $2^{n - 1}$ sovereigns in bag $n$.
Put the remaining $489$ in bag $10$.
== Proof ==
A thinly-disguised implementation of the Basis Representation Theorem for binary.
== Sources ==
* : Solutions: $11$. -- The Perplexed Banker
* : Answers: $7$. The Perplexed Banker
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/120 - The Ribbon Pentagon

== by : $120$ ==
;The Ribbon Pentagon
:The solution to the following will be found very interesting if the reader has not seen it before.
:I want to form a regular pentagon, but the only thing at hand happens to be a rectangular strip of paper.
::How am I to do it without pencil, compasses, scissors, or anything else whatever but my fingers?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Paper-Folding Puzzles: $120$. -- The Ribbon Pentagon
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/120 - The Ribbon Pentagon/Solution

== by : $120$ ==
;The Ribbon Pentagon
== Solution ==
This is demonstrated in Trefoil Knot in Paper forms Pentagon:
:
== Also see ==
* Henry Ernest Dudeney: Puzzles and Curious Problems $222$ - Folding a Pentagon
== Sources ==
* : Solutions: $120$. -- The Ribbon Pentagon
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/121 - Paper Folding

== by : $121$ ==
;Paper Folding
:This is a branch of puzzledom both instructive and interesting.
:I do not refer to folding paper into the forms of boxes, boats, frogs, and such things,
::for these are toys rather than puzzles,
::but to the solving of certain geometric problems with paper and fingers alone.
:I will give a comparatively easy example.
:Suppose you are given a perfectly square piece of paper,
::how are you going to fold it so as to indicate by creases a regular hexagon,
:as shown in the illustration, all ready to be cut out?
:
:Of course, you must use no pencil, measure, or instrument of any kind whatever.
:The hexagon may be in any position in the square.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Paper-Folding Puzzles: $121$. -- Paper Folding
* : Geometrical Problems: Paper Folding Puzzles: $361$. Folding a Hexagon
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/121 - Paper Folding/Solution

== by : $121$ ==
;Paper Folding
== Solution ==
:
Fold the square through the midpoints of opposite sides to get the folds $AOB$ and $COD$.
Fold $EH$ and $FG$ so as to bisect $AO$ and $OB$.
Make the fold $AJ$ through $A$ so that the vertex $K$ lies on $EH$ at $H$.
$H$ is one of the vertices of the hexagon.
Fold $HG$ to make that side.
Make the other vertices of the hexagon similarly.
The rest follows.
== Sources ==
* : Solutions: $121$. -- Paper Folding
* : Answers: $361$. Folding a Hexagon
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions
Henry Ernest Dudeney/Modern Puzzles/122 - Folding a Pentagon

== by : $122$ ==
;Folding a Pentagon
:Here is another puzzle in paper folding of a rather more difficult character than the hexagon example that we have considered.
:If you are given a perfectly square piece of paper,
::how are you going to fold it so as to indicate by creases a regular pentagon,
:all ready to be cut out?
:
:Remember that you must use your fingers only, without any instrument or measure whatever.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Paper-Folding Puzzles: $122$. -- Folding a Pentagon
* : Geometrical Problems: Paper Folding Puzzles: $362$. Folding a Pentagon
Category:Henry Ernest Dudeney/Modern Puzzles
Henry Ernest Dudeney/Modern Puzzles/122 - Folding a Pentagon/Solution

== by : $122$ ==
;Folding a Pentagon
== Solution ==
Take the square $\Box ABCD$.
:
Fold $\Box ABCD$ in half horizontally so $A$ lies on $B$ to get the midpoint $E$ of $AB$.
Fold $EC$.
Fold $EF$ to make $B$ lie on $EC$ at $G$.
Fold $CB$ onto $CE$ to make $H$ lie on $G$.
Fold $AB$ at $K$ to make $B$ lie on $H$.
Fold $\Box ABCD$ in half vertically along $PQ$ so as to make $K$ lie on $L$.
$BC$ is now said to be divided in medial section.
$KL$ is one of the sides of the regular pentagon.
Fold at $K$ so that $L$ lies on $AB$ at $M$.
Fold at $L$ so that $K$ lies on $CD$ at $N$.
Fold at $M$ so that $K$ lies on $PQ$ at $O$.
We can also fold at $N$ so that $L$ also lies on $PQ$ at $O$.
Folding $KM$, $LN$, $MO$ and $NO$ completes the construction.
== Historical Note ==
== Sources ==
* : Solutions: $122$. -- Folding a Pentagon
* : Answers: $362$. Folding a Pentagon
Category:Henry Ernest Dudeney/Modern Puzzles/Solutions