nyuuzyou/wikis huggingface dataset:
Henry Ernest Dudeney/Puzzles and Curious Problems/176 - Counting the Loss/Mistake

== Source Work ==
:
:Arithmetical and Algebraical Problems
::Various Arithmetical and Algebraical Problems
:::$176$. -- Counting the Loss
:
:Arithmetical and Algebraical Problems
::Miscellaneous Puzzles
:::$240$. Counting the Loss
== Mistake ==
:The general solution of this is obtained from the indeterminate equation
::$\dfrac {35 x - 48} {768}$
:which must be an integer, where $x$ is the number of survivors.
== Correction ==
The equation ought to be:
:$\dfrac {35 x - 48} {256}$
== Sources ==
* : Solutions: $176$. -- Counting the Loss
* : Answers: $240$. Counting the Loss
Category:Mistakes/Puzzles and Curious Problems
Category:Mistakes/536 Puzzles & Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/176 - Counting the Loss/Solution

== by : $176$ ==
;Counting the Loss
== Solution ==
There were $472$ soldiers who were killed in the engagement.
== Proof ==
Let $n$ be the number of survivors of the engagement.
Let $n_1$, $n_2$ and $n_3$ be the numbers left in the captured group at the end of days $1$ to $3$ respectively.
We have:
This leads us to the linear Diophantine equation:
:$35 n - 256 k = 48$
From Example of Linear Diophantine Equation: $35 x - 256 y = 48$:
:$n = 16 + 256 t, k = 2 + 35 t$
for $t \in \Z$.
We now need to select a value of $t$ such that:
:$1 \le n \le 1000$
and:
:$6 \divides n$
in order to fit the conditions of the question.
By inspection of the cases where $t = 0, 1, 2, 3, 4$ we have that the only solution is for $t = 2$.
Thus:
:$n = 16 + 256 \times 2 = 528$
That is, there were $528$ survivors of the initial combat.
Hence $1000 - 528 = 472$ men died in battle.
The result follows.
== Sources ==
* : Solutions: $176$. -- Counting the Loss
* : Answers: $240$. Counting the Loss
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/177 - Square of Squares

== by : $177$ ==
;Square of Squares
:Cutting only along the lines, what is the smallest number of square pieces into which the diagram can be dissected?
:
:The largest number possible is, of course, $169$, where all the pieces will be of the same size -- one cell -- but we want the smallest number.
:We might cut away the border on two sides, leaving one square $12 \times 12$, and cutting the remainder into $25$ little squares, making $25$ in all.
:This is better than $169$, but considerably more than the fewest possible.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $177$. -- Square of Squares
* : Geometrical Problems: Dissection Puzzles: $343$. Square of Squares
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/177 - Square of Squares/Historical Note

== Historical Note on by : $177$ - Square of Squares ==
This puzzle also appears in 's $1917$ collection , under the title $173$ - Mrs. Perkins's Quilt.
The problem had previously appeared in $1907$ in the first issue of , edited by .
This was later published in 's pusthumous collection .
If stole it from , then must have published it somewhere before $1907$.
 reports in $1968$ that the general problem of dividing a square lattice of any size along lattice lines into the smallest number of squares has been discussed but not solved in several places, including by him.
The corresponding problem on a triangular lattice, he reports, had not been studied at that time.
== Sources ==
* 
* 
* 
* : Answers: $343$. Square of Squares
* : $11$: Mrs. Perkins' Quilt and Other Square-Packing Problems
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/177 - Square of Squares/Solution

== by : $177$ ==
;Square of Squares
== Solution ==
:
:The fewest pieces must be $11$, and the solution (barring reflection of the section with the $8$ smaller squares) is unique.
== Historical Note ==
== Sources ==
* : Solutions: $177$. -- Square of Squares
* : Answers: $343$. Square of Squares
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/178 - Stars and Crosses

== by : $178$ ==
;Stars and Crosses
:Cut the square into four parts by going along the lines, so that each part shall be exactly the same size and shape,
::and each part contains a star and a cross.
:
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $178$. -- Stars and Crosses
* : Geometrical Problems: Dissection Puzzles: $344$. Stars and Crosses
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/178 - Stars and Crosses/Solution

== by : $178$ ==
;Stars and Crosses
== Solution ==
:
== Also see ==
* Puzzles and Curious Problems: $196$ - The Four Stars, which is exactly the same puzzle as this, presented slightly differently.
== Sources ==
* : Solutions: $178$. -- Stars and Crosses
* : Answers: $344$. Stars and Crosses
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/179 - Greek Cross Puzzle

== by : $179$ ==
;Greek Cross Puzzle
:Cut the square into four pieces as shown, and put them together to form a regular Greek cross.
:
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $179$. -- Greek Cross Puzzle
* : Geometrical Problems: Dissection Puzzles: $345$. Greek Cross Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/17 - The Missing Penny

== by : $17$ ==
;The Missing Penny
:Here is an ancient puzzle that has always perplexed some people.
: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?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $17$. -- The Missing Penny
* : Arithmetical and Algebraical Problems: Money Puzzles: $23$. The Missing Penny
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/17 - The Missing Penny/Solution

== by : $17$ ==
;The Missing Penny
== Solution ==
This is an instance of the Applesellers' Problem.
== Sources ==
* : Solutions: $17$. -- The Missing Penny
* : Answers: $23$. The Missing Penny
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Category:Applesellers' Problem
Henry Ernest Dudeney/Puzzles and Curious Problems/180 - Square and Cross

== by : $180$ ==
;Square and Cross
:Cut a regular Greek cross into five pieces,
::so that one piece shall be a smaller regular Greek cross,
::and so that the remaining four pieces will fit together and form a perfect square.
:
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $180$. -- Square and Cross
* : Geometrical Problems: Dissection Puzzles: $346$. Square and Cross
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/181 - Three Greek Crosses from One

== by : $181$ ==
;Three Greek Crosses from One
:How can you cut a regular Greek cross into as few pieces as possible
::so as to reassemble them into $3$ identical smaller regular Greek crosses?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $181$. -- Three Greek Crosses from One
* : Geometrical Problems: Dissection Puzzles: $347$. Three Greek Crosses from One
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/181 - Three Greek Crosses from One/Solution

== by : $181$ ==
;Three Greek Crosses from One
== Solution ==
Cut the upper and lower arms $A$ and $B$ off the Greek cross and lay them alongside the remainder to make a long rectangle.
Then cut the larger piece to get $C$, $D$ and $E$ and make the rectangle shown:
:
Then you cut that rectangle up as follows:
:
and hey presto.
Unconvincing.
== Historical Note ==
== Sources ==
* : Solutions: $181$. -- Three Greek Crosses from One
* : Answers: $347$. Three Greek Crosses from One
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/182 - Making a Square

== by : $182$ ==
;Making a Square
:Here is an elegant, but not difficult, little cutting-out puzzle that will interest readers (sent by ).
:Cut the figure into four pieces, each of the same size and shape,
::that will fit together to form a perfect square.
:
=== Click here for solution ===
== Historical Note ==
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $182$. -- Making a Square
* : Geometrical Problems: Dissection Puzzles: $348$. Making a Square
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/183 - Table-Top and Stools

== by : $183$ ==
;Table-Top and Stools
:Some people may be familiar with the old puzzle of the circular table-top cut into pieces to form two oval stools, each with a hand-hole.
:
:Those who remember the puzzle will be interested in a solution in as few as four pieces by the late .
:Can you cut the circle into four pieces that will fit together (two and two) and form two oval stool-tops, each with a hand-hole?
=== Click here for solution ===
== Historical Note ==
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $183$. -- Table-Top and Stools
* : Geometrical Problems: Dissection Puzzles: $349$. Table-Top and Stools
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/183 - Table-Top and Stools/Historical Note

== Historical Note on by : $183$ - Table-Top and Stools ==
:The old solution was in $8$ pieces, but an improved version was given in only $6$ pieces in , No. $157$.
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $183$. -- Table-Top and Stools
* : Geometrical Problems: Dissection Puzzles: $349$. Table-Top and Stools
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/183 - Table-Top and Stools/Solution

== by : $183$ ==
;Table-Top and Stools
== Solution ==
:Figure $A$ shows the circle divided into four equal pieces, forming the Great Monad,
::and in Figure $B$ we have two pieces reassembled to form one of the two stools,
::the other two being similarly constructed from $3$ and $4$.
:
:Unfortunately the hand-holes are across instead of lengthways,
::but no condition is broken.
== Sources ==
* : Solutions: $183$. -- Table-Top and Stools
* : Answers: $349$. Table-Top and Stools
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/184 - Dissecting the Letter E

== by : $184$ ==
;Dissecting the Letter $\text E$
:In readers were asked to cut this $\text E$ into five pieces
::that would fit together and form a perfect square.
:
:It was understood that no piece was to be turned over,
::but we remarked that it can be done in four pieces if you are allowed to turn over pieces.
:I give the puzzle again, with permission to make the reversals.
:Can you do it in four pieces?
:We have given all the measurements, so there shall be no doubt as to the correct proportions of the letter.
=== Click here for solution ===
== Also see ==
* Modern Puzzles: $107$ - Dissecting the Letter $\text E$
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $184$. -- Dissecting the Letter $\text E$
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/184 - Dissecting the Letter E/Solution

== by : $184$ ==
;Dissecting the Letter $\text E$
== Solution ==
:
Piece $D$ has been turned over.
== Sources ==
* : Solutions: $184$. -- Dissecting the Letter $\text E$
* : Answers: $330$. Dissecting the Letter $\text E$
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/185 - The Dissected Chessboard

== by : $185$ ==
;The Dissected Chessboard
:Here is an ancient and familiar fallacy.
:If you cut a chessboard into four pieces in the manner indicated by the black lines in Figure $\text A$,
::and then reassemble the pieces as in Figure $\text B$,
::you appear to gain a square by the operation,
::since this second figure would seem to contain $13 \times 5 = 65$ squares.
:
:I have explained this fallacy over and over again, and the reader probably understands all about it.
:The present puzzle is to place the same four pieces together in another way
::so that it may appear to the novice that instead of gaining a square we have lost one,
::the new figure apparently containing only $63$ cells.
:It is best to use the diagram that is not chequered in black and white cells.
=== Click here for solution ===
== Also see ==
* Sam Loyd's Missing Square, upon which this entry was based
* Puzzles and Curious Problems: $189$ - Problem of the Extra Cell, where he raises the initial problem once more.
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $185$. -- The Dissected Chessboard
* : Geometrical Problems: Dissection Puzzles: $353$. Problem of the Missing Cell
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Sam Loyd's Missing Square
Henry Ernest Dudeney/Puzzles and Curious Problems/185 - The Dissected Chessboard/Solution

== by : $185$ ==
;The Dissected Chessboard
== Solution ==
:
== Also see ==
* Sam Loyd's Missing Square
* Puzzles and Curious Problems: $189$ - Problem of the Extra Cell, where he raises the initial problem once more.
== Sources ==
* : Solutions: $185$. -- Dissected Chessboard
* : Answers: $353$. Problem of the Missing Cell
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/186 - Triangle and Square

== by : $186$ ==
;Triangle and Square
:Can you cut each of two equilateral triangles into three pieces,
::so that the six pieces will fit together and form a perfect square?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $186$. -- Triangle and Square
* : Geometrical Problems: Dissection Puzzles: $350$. Triangle and Square
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/186 - Triangle and Square/Solution

== by : $186$ ==
;Triangle and Square
== Solution ==
Cut one triangle in half, and place the pieces together as in Figure $1$.
:
Now cut along the dotted lines, making $ab$ and $cd$ each equal to the side of the square we are making.
Then fit together the pieces as in Figure $2$, sliding the pieces $F$ and $C$ upwards to the left, bringing down $D$ to fill that gap in the corner.
== Historical Note ==
== Sources ==
* : Solutions: $186$. -- Triangle and Square
* : Answers: $350$. Triangle and Square
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/187 - Changing the Suit

== by : $187$ ==
;Changing the Suit
:You are asked to cut the Spade into three pieces that will fit together and form a Heart.
:
:Of course, no part of the material may be wasted, or it would be absurd,
::since it would be necessary merely to cut away the stem of the Spade.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $187$. -- Changing the Suit
* : Geometrical Problems: Dissection Puzzles: $351$. Changing the Suit
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/187 - Changing the Suit/Solution

== by : $187$ ==
;Changing the Suit
== Solution ==
:The diagram shows how the Spade may be cut into three parts that will fit together and form a Heart.
:
== Sources ==
* : Solutions: $187$. -- Changing the Suit
* : Answers: $351$. Changing the Suit
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle

== by : $188$ ==
;Squaring the Circle
:The problem of squaring the circle depends on finding the ratio of the diameter to the circumference.
:This cannot be found in numbers with exactitude,
::but we can get near enough for all practical purposes.
:But it is equally impossible, by Euclidean geometry, to draw a straight line equal to the circumference of a given circle.
:You can roll a penny carefully on its edge along a straight line on a sheet of paper and get a pretty exact result,
::but such a thing as a circular garden-bed cannot be so rolled.
:Now, the line below, when straightened out
::(it is bent for convenience in presentation),
::is very nearly the exact length of the circumference of the accompanying circle.
:
:The horizontal part of the line is half the circumference.
:Could you have found it by a simple method, using only pencil, compasses and ruler?
=== Click here for solution 1 ===
=== Click here for solution 2 ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $188$. -- Squaring the Circle
* : Geometrical Problems: Circle Puzzles: $289$. Squaring the Circle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle
Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle/Mistake

== Source Work ==
:
:Geometrical Problems
::Dissection Puzzles
:::$188$. -- Squaring the Circle
:
:Geometrical Problems
::Circle Puzzles
:::$289$. Squaring the Circle
== Mistake ==
:The distance $DG$, added to the distance $GH$, gives a quarter of the length of the circumference, correct within a five-thousandth part.
== Correction ==
:$\dfrac {1.571174 - 1.570796} {1.571174} \approx 4155$
That is, it is correct within a $4000$th part, but not a $5000$th part.
== Sources ==
* : Solutions: $188$. -- Squaring the Circle
* : Answers: $289$. Squaring the Circle
Category:Mistakes/Puzzles and Curious Problems
Category:Mistakes/536 Puzzles & Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle/Solution 1

== by : $188$ ==
;Squaring the Circle
== Solution ==
Make a rectangle with one side equal to the diameter and one side $3$ times the diameter.
Then take the diagonal of this rectangle.
This will be quite close to the circumference, as it is $\sqrt {10}$ or approximately $3.162$ times the diameter.
== Sources ==
* : Solutions: $188$. -- Squaring the Circle
* : Answers: $289$. Squaring the Circle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle
Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle/Solution 2

== by : $188$ ==
;Squaring the Circle
== Solution ==
:
$AB$ is the diameter of the circle whose center is at $C$.
Bisect the semicircle $AB$ at $D$.
Construct $AE = AC$ and $BF = BC$.
Construct $DE$ and $DF$.
Let $DE$ and $DF$ intersect $AB$ and $G$ and $H$.
Then $DG + GH$ is one quarter the length of the circumference of the circle within a $\dfrac 1 {4000}$ part.
== Proof ==
Notice that the above diagram is symmetrical.
Therefore $DC \perp AB$.
Let the radius of the circle be $r$.
Denote the foot of the perpendicular from $E$ to $AB$ be $P$.
Since $CA = CE = AC$, $\triangle ACE$ is equilateral.
Hence $AP = PC = \dfrac r 2$ and $EP = \dfrac {\sqrt 3} 2 r$.
$\triangle PEH \sim \triangle CDH$ as Equiangular Triangles are Similar.
Therefore $\dfrac {DC} {EP} = \dfrac {CH} {PH} = \dfrac 2 {\sqrt 3}$.
We can now obtain:
:$CH = \dfrac r 2 \times \dfrac 2 {2 + \sqrt 3} = \dfrac r {2 + \sqrt 3}$
By Pythagoras' Theorem:
:$DG = DH = \sqrt {\paren {\dfrac r {2 + \sqrt 3} }^2 + r^2} = \dfrac r {2 + \sqrt 3} \sqrt {8 + 4 \sqrt 3}$
Now we can calculate $DG + GH$:
The fraction:
:$\dfrac {2 \paren {1 + \sqrt {2 + \sqrt 3} } } {2 + \sqrt 3} \approx 1.571174 \ldots$
is a close approximation to:
:$\dfrac \pi 2 \approx 1.570796 \ldots$
== Sources ==
* : Solutions: $188$. -- Squaring the Circle
* : Answers: $289$. Squaring the Circle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle
Henry Ernest Dudeney/Puzzles and Curious Problems/189 - Problem of the Extra Cell

== by : $189$ ==
;Problem of the Extra Cell
Here is a fallacy that is widely known but imperfectly explained.
:Doubtless many readers will recognize it, and some of them have probably been not a little perplexed.
:In diagram $A$ the square representing a chessboard is cut into $4$ pieces along the dark lines,
::and these four pieces are seen re-assembled in Diagram $B$.
:
:But in $A$ we have $64$ of these little squares, whereas in $B$ we have $65$.
:Where does the additional cell come from?
:Examine it carefully and see if you can discover whether it is really possible that you can increase the size of a slice of bread and butter
::merely by cutting it into pieces and putting them together again differently.
=== Click here for solution ===
== Also see ==
* Sam Loyd's Missing Square
* $185$ - The Dissected Chessboard in the same collection.
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $189$. -- Problem of the Extra Cell
* : Geometrical Problems: Dissection Puzzles: $352$. Problem of the Extra Cell
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Sam Loyd's Missing Square
Henry Ernest Dudeney/Puzzles and Curious Problems/189 - Problem of the Extra Cell/Historical Note

== Historical Note on by : $189$ - Problem of the Extra Cell ==
 discusses this and several other paradoxes of a similar type in his from $1956$, in chapters $7$ and $8$: Geometrical Vanishes, parts $\text I$ and $\text {II}$.
== Sources ==
* : Answers: $352$. Problem of the Extra Cell
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/189 - Problem of the Extra Cell/Solution

== by : $189$ ==
;Problem of the Extra Cell
== Solution ==
:
== Also see ==
* Sam Loyd's Missing Square
* Puzzles and Curious Problems: $185$ - The Dissected Chessboard, where the question is raised again from a different angle.
== Historical Note ==
== Sources ==
* : Solutions: $189$. -- Problem of the Extra Cell
* : Chapter $8$ - Geometrical Vanishes -- Part $\text {II}$: Square Variation
* : Answers: $352$. Problem of the Extra Cell
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/18 - The Red Death League

== by : $18$ ==
;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 $\pounds 313, 5 \shillings 4 \tfrac 1 4 \oldpence$
:We are also given that the number of members is under $500$.
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $18$. -- The Red Death League
* : Arithmetical and Algebraical Problems: Money Puzzles: $24$. The Red Death League
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/18 - The Red Death League/Solution

== by : $18$ ==
;The Red Death League
== Solution ==
:$311$ members, each paying dues of $\pounds 1, 0 \shillings 1 \tfrac 3 4 \oldpence$
== Proof ==
We convert $\pounds 313, 5 \shillings 4 \tfrac 1 4 \oldpence$ into farthings:
Thus there were $311$ members, and the dues were $967$ farthings.
Hence the result, after conversion back into pounds, shillings and pence.
== Sources ==
* : Solutions: $18$. -- The Red Death League
* : Answers: $24$. The Red Death League
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions