nyuuzyou/wikis huggingface dataset:
Henry Ernest Dudeney/Puzzles and Curious Problems/190 - A Horseshoe Puzzle

== by : $190$ ==
;A Horseshoe Puzzle
:Here is an easy little puzzle, but we have seen people perplexed by it for some time.
:Given a paper horseshoe, similar to the one in the illustration,
::can you cut it into seven pieces, with two straight clips of the scissors,
::so that each part shall contain a nail hole?
:
:There is no objection to your shifting the pieces and putting them together after the first cut,
::only you must not bend or fold the paper in any way.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $190$. -- A Horseshoe Puzzle
* : Geometrical Problems: Dissection Puzzles: $354$. A Horseshoe Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/190 - A Horseshoe Puzzle/Solution

== by : $190$ ==
;A Horseshoe Puzzle
== Solution ==
:
:First make cut $AB$.
:Then so place the three pieces together that with one clip of the scissors you can make the cut $CD$ together with $EF$ and $GH$.
== Sources ==
* : Solutions: $190$. -- A Horseshoe Puzzle
* : Answers: $354$. A Horseshoe Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/191 - Two Squares in One

== by : $191$ ==
;Two Squares in One
:Two squares of any relative size can be cut into $5$ pieces, in the manner shown below,
::that will fit together and form a larger square.
:
:But this involves cutting the smaller square.
:Can you show an easy method of doing it without in any way cutting the smaller square?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $191$. -- Two Squares in One
* : Geometrical Problems: Dissection Puzzles: $356$. Two Squares in One
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/191 - Two Squares in One/Historical Note

== Historical Note on by : $191$ - Two Squares in One ==
This dissection was discovered by in about $1830$, and published by him in $1873$.
 reports on it in detail in his $1966$ collection 
== Sources ==
* : $5$: Paper Cutting
* : Answers: $356$. Two Squares in One
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/191 - Two Squares in One/Solution

== by : $191$ ==
;Two Squares in One
== Solution ==
:
Place the two squares together so that $AB$ and $CD$ are straight lines.
Locate the centre point of the larger square.
Draw $AD$
Draw $EF$ and $GH$ through that centre point parallel to and perpendicular to $AD$ respectively.
Then you can cut out pieces $1$, $2$, $3$ and $4$, which, together with the smaller square $5$, fit together to form the big square of side $AD$.
== Historical Note ==
== Sources ==
* : Solutions: $191$. -- Two Squares in One
* : Answers: $356$. Two Squares in One
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/192 - The Submarine Net

== by : $192$ ==
;The Submarine Net
:The illustration is supposed to represent a portion of a long submarine net,
::and the puzzle is to make as few cuts as possible from top to bottom,
::to divide the net into two parts,
::and so to make an opening for a submarine to pass through.
:
:Where would you make the cuts?
:No cut can be made through the knots.
:Only remember the cuts must be made from the top line to the bottom.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $192$. -- The Submarine Net
* : Combinatorial & Topological Problems: Route & Network Puzzles: $418$. The Submarine Net
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/192 - The Submarine Net/Solution

== by : $192$ ==
;The Submarine Net
== Solution ==
:
The $8$ cuts that are needed are shown in red.
== Sources ==
* : Solutions: $192$. -- The Submarine Net
* : Answers: $418$. The Submarine Net
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/193 - Square Table-Top

== by : $193$ ==
;Square Table-Top
:The illustration represents a $7 \times 7$ piece of veneer which has been cut into a number of pieces,
::of which the shaded pieces are unusable.
:A cabinet maker had to fit together the remaining $8$ pieces of veneer to form a small square table-top, $6 \times 6$,
:and he stupidly cut that piece No. $8$ into three parts.
:
:How would you form the square without cutting any one of the pieces?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $193$. -- Square Table-Top
* : Geometrical Problems: Dissection Puzzles: $355$. Square Table Top
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/194 - Cutting the Veneer

== by : $194$ ==
;Cutting the Veneer
:A cabinetmaker had a perfect square of beautiful veneer
::which he wished to cut into $6$ pieces to form three separate squares, all different sizes.
:How might this have been done without any waste?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $194$. -- Cutting the Veneer
* : Geometrical Problems: Dissection Puzzles: $357$. Cutting the Veneer
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/194 - Cutting the Veneer/Historical Note

== Historical Note on by : $194$ - Cutting the Veneer ==
's reports that has discovered many $5$-piece dissections, one with cut length of $16$.
He offers it up as a challenge to his readers to find the latter.
== Sources ==
* : Answers: $357$. Cutting the Veneer
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/194 - Cutting the Veneer/Solution

== by : $194$ ==
;Cutting the Veneer
== Solution ==
:
Squares $A$ and $B$ are cut out entire.
Pieces $C$, $D$, $E$ and $F$ are then used to make the third square.
== Historical Note ==
== Sources ==
* : Solutions: $194$. -- Cutting the Veneer
* : Answers: $357$. Cutting the Veneer
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/195 - Improvised Chessboard

== by : $195$ ==
;Improvised Chessboard
:Cut this piece of checkered linoleum into only two pieces,
::that will fit together and form a perfect chessboard,
::without disturbing the checkering of black and white.
:
:Of course, it would be easy to cut off those two overhanging white squares and put them in the vacant places,
::but that would be doing it in three pieces.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $195$. -- Improvised Chessboard
* : Geometrical Problems: Dissection Puzzles: $358$. Improvised Chessboard
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/195 - Improvised Chessboard/Solution

== by : $195$ ==
;Improvised Chessboard
== Solution ==
:
== Sources ==
* : Solutions: $195$. -- Improvised Chessboard
* : Answers: $358$. Improvised Chessboard
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/196 - The Four Stars

== by : $196$ ==
;The Four Stars
:Can you cut the square into four pieces, all of exactly the same size and shape,
::each piece to contain a star, and each piece to contain one of the four central squares?
:
:The cuts must all pass along the lines, a condition that simplifies the puzzle rather than adds to its difficulty.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $196$. -- The Four Stars
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/196 - The Four Stars/Solution

== by : $196$ ==
;The Four Stars
== Solution ==
:
== Also see ==
* Puzzles and Curious Problems: $178$ - Stars and Crosses, which is exactly the same puzzle as this, presented slightly differently.
== Sources ==
* : Solutions: $196$. -- The Four Stars
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/197 - Economical Dissection

== by : $197$ ==
;Economical Dissection
:Take a block of wood $8$ units long by $4$ units wide by $3 \tfrac 3 4$ units deep.
:How many pieces, each measuring $2 \tfrac 1 2$ by $1 \tfrac 1 2$ by $1 \tfrac 1 4$ can be cut out of it?
:Most people would have more waste material left over than is necessary.
:How many pieces may be cut from the block?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Dissection Puzzles: $197$. -- Economical Dissection
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/197 - Economical Dissection/Solution

== by : $197$ ==
;Economical Dissection
== Solution ==
:Even though the volume of the block is enough to make $25$ pieces, you can in fact make only $24$.
:Reduce the length of the block by half a unit.
:The smaller piece off the end cannot be used.
:Then cut the larger piece into $3$ slabs, each $1 \tfrac 1 4$ units thick.
:Eight blocks can then be cut from each slab.
== Sources ==
* : Solutions: $197$. -- Economical Dissection
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/198 - The Patchwork Cushion

== by : $198$ ==
;The Patchwork Cushion
:A lady had $20$ pieces of silk, all of the same triangular shape and size.
:She found that four of these would fit together and form a perfect square, as in the illustration.
:
:How was she to fit together these $20$ pieces to form a perfectly square patchwork cushion?
:There must be no waste, and no allowance need be made for turnings.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Patchwork Puzzles: $198$. -- The Patchwork Cushion
* : Geometrical Problems: Dissection Puzzles: $359$. The Patchwork Cushion
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/198 - The Patchwork Cushion/Solution

== by : $198$ ==
;The Patchwork Cushion
== Solution ==
:
== Sources ==
* : Solutions: $198$. -- The Patchwork Cushion
* : Answers: $359$. The Patchwork Cushion
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/199 - The Hidden Star

== by : $199$ ==
;The Hidden Star
:The illustration represents a square tablecloth of choice silk patchwork.
:This was put together by the members of a family as a little birthday present for one of its number.
:One of the contributors supplied a portion in the form of a perfectly symmetrical star,
::and this has been worked in exactly as it was received.
:
:But the triangular pieces so confuse the eye that it is quite a puzzle to find the hidden star.
:Can you discover it, so that, if you wished, by merely picking put the stitches,
::you could extract it from the other portions of the patchwork?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Patchwork Puzzles: $199$. -- The Hidden Star
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $267$. The Hidden Star
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/199 - The Hidden Star/Solution

== by : $199$ ==
;The Hidden Star
== Solution ==
:
:it is surprising how bewildering it is to find the star until you have been once shown it, or have found it,
::and then it will appear pretty obvious.
== Sources ==
* : Solutions: $199$. -- The Hidden Star
* : Answers: $267$. The Hidden Star
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/19 - A Poultry Poser

== by : $19$ ==
;A Poultry Poser
:Three chickens and one duck sold for as much as two geese;
::one chicken, two ducks, and three geese were sold together for $25 \shillings$
:What was the price of each bird in an exact number of shillings?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $19$. -- A Poultry Poser
* : Arithmetical and Algebraical Problems: Money Puzzles: $25$. A Poultry Poser
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/19 - A Poultry Poser/Solution

== by : $19$ ==
;A Poultry Poser
== Solution ==
A chicken costs $2 \shillings$, a duck costs $4 \shillings$ and a goose costs $5 \shillings$
== Proof ==
Let $c$, $d$ and $g$ be the price in shillings for one chicken, one duck and one goose respectively.
We have:
It follows that $g$ is a multiple of $5$.
If $g \ge 10$ we have from $(2)$ that $c + 2 d < 0$ which cannot happen.
Hence $g = 5$ and so:
== Sources ==
* : Solutions: $19$. -- A Poultry Poser
* : Answers: $25$. A Poultry Poser
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/1 - The Money Bag

== by : $1$ ==
;The Money Bag
:"A bag," said Rackbrane, when helping himself to the marmalade, "contained fifty-five coins consisting entirely of crowns and shillings,
::and their total value was $\pounds 7, \ 3 \shillings 0 \oldpence$
:How many coins were there of each kind?"
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $1$. -- The Money Bag
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/1 - The Money Bag/Solution

== by : $1$ ==
;The Money Bag
== Solution ==
:$22$ crowns and $33$ shillings.
== Proof ==
Let $c$ and $s$ be the number of crowns and shillings respectively.
Recall that:
:$1$ crown is worth $5$ shillings
:$1$ pound is worth $20$ shillings.
Hence:
== Sources ==
* : Solutions: $1$. -- The Money Bag
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/200 - Measuring the River

== by : $200$ ==
;Measuring the River
:A traveller reaches a river at the point $A$,
::and wishes to know the width across to $B$.
:
:As he has no means of crossing the river, what is the easiest way of finding its width?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $200$. -- Measuring the River
* : Geometrical Problems: Plane Geometry Puzzles: $306$. Measuring the River
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/200 - Measuring the River/Solution

== by : $200$ ==
;Measuring the River
== Solution ==
The initial assumption is made that it is possible to identify features on the opposite bank of the river, and to identify when one is exactly opposite such a feature.
It is also assumed that the traveller has the basic surveying apparatus necessary.
:
We have been given that $A$ is directly opposite point $B$, which can thus be identified.
Measure an arbitrary distance $AC$ along the river bank perpendicular to $AB$.
Then measure another arbitrary distance $CD$ similarly perpendicular to $AC$.
Then locate the point $E$, which is where $AC$ and $DB$ cross.
The triangles $\triangle ABE$ and $\triangle CDE$ are then similar.
The distance $AB$ can then be determined by elementary geometry.
== Sources ==
* : Solutions: $200$. -- Measuring the River
* : Answers: $306$. Measuring the River
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/201 - Square and Triangle

== by : $201$ ==
;Square and Triangle
:Take a perfectly square piece of paper,
::and fold it as to form the largest possible equilateral triangle.
:A triangle in which the sides are the same length as those of the square, as shown in our diagram,
::will not be the largest possible.
:
:Of course, no markings or measurements may be made except by the creases themselves.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $201$. -- Square and Triangle
* : Geometrical Problems: Paper Folding Puzzles: $364$. Square and Triangle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/201 - Square and Triangle/Solution

== by : $201$ ==
;Square and Triangle
== Solution ==
Fold the square in half to get the crease $EF$.
:
Fold along $AH$ to get $B$ to lie on $EF$ at $G$.
With that fold in place, fold $HGJ$.
While $B$ is on $G$, fold $AB$ back on $AH$ to get the line $AK$.
You can now fold the triangle $AJK$, which is the largest possible equilateral triangle that can be obtained.
== Sources ==
* : Solutions: $201$. -- Square and Triangle
* : Answers: $364$. Square and Triangle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/202 - A Garden Puzzle

== by : $202$ ==
;A Garden Puzzle
:The four sides of a garden are known to be $20$, $16$, $12$ and $10$ rods,
::and it has the greatest possible area for these sides.
:What is the area?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $202$. -- A Garden Puzzle
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $268$. A Garden Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/202 - A Garden Puzzle/Solution

== by : $202$ ==
;A Garden Puzzle
== Solution ==
Approximately $194.4$ square rods.
== Proof ==
Let $\AA$ square rods be the area of the garden.
We are given that $\AA$ is the greatest possible for the given sides.
From Area of Quadrilateral with Given Sides is Greatest when Quadrilateral is Cyclic, the quadrilateral formed by the sides of the garden is cyclic.
Hence we can apply Brahmagupta's Formula:
:$\AA = \sqrt {\paren {s - a} \paren {s - b} \paren {s - c} \paren {s - d} }$
where $s$ is the semiperimeter:
:$s = \dfrac {a + b + c + d} 2$
Thus:
and so:
== Also see ==
* $130$ - Mr. Grindle's Garden in 's collection of $1926$, which is the same as this but for the specific numbers.
== Sources ==
* : Solutions: $202$. -- A Garden Puzzle
* : Answers: $268$. A Garden Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/203 - A Triangle Puzzle

== by : $203$ ==
;A Triangle Puzzle
:In the solution to our puzzle No. $162$, we said that:
::"there is an infinite number of rational triangles composed of three consecutive numbers like $3$, $4$, $5$, and $13$, $14$, $15$."
:We here show these two triangles.
:
:In the first case the area ($6$) is half of $3 \times 4$,
::and in the second case, the height being $12$, the area ($84$) is a half of $12 \times 14$.
:It will be found interesting to discover such a triangle with the smallest possible three consecutive numbers for its sides,
::that has an area that may be exactly divided by $20$ without remainder.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $203$. -- A Triangle Puzzle
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $269$. A Triangle Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Heronian Triangles
Henry Ernest Dudeney/Puzzles and Curious Problems/203 - A Triangle Puzzle/Solution

== by : $203$ ==
;A Triangle Puzzle
== Solution ==
The triangle whose sides are $2701$, $2702$ and $2703$ has an area of $3 \, 161 \, 340$.
== Proof ==
Extend the following table as you like:
:$\begin{array} {rrrrr}
n & p_n & q_n & \text{Height} & \text{Area} \\ \hline
1 & 2 & 4 & 3 & 6 \\
2 & 8 & 14 & 12 & 84 \\
3 & 30 & 52 & 45 & 1170 \\
4 & 112 & 194 & 168 & 16 \, 296 \\
5 & 418 & 724 & 627 & 226 \, 974 \\
6 & 1560 & 2702 & 23490 & 3 \, 161 \, 340 \\
\end {array}$
This table is governed by the recurrence relation:
:$p_n = \begin {cases} 0 & : n = 0 \\ 2 & : n = 1 \\ 4 p_{n - 1} - p_{n - 2} \end {cases}$
and:
:${q_n}^2 = 3 {p_n}^2 + 4$
Each row describes a triangle $T$ whose sides are consecutive integers $q - 1$, $q$, $q + 1$, such that:
:the height of $T$ is equal to $\dfrac {3 P} 2$
:the area of $T$ is equal to the height multiplied by $\dfrac q 2$.
This is demonstrated in Approximations to Equilateral Triangles by Heronian Triangles, except it's not.
== Sources ==
* : Solutions: $203$. -- A Triangle Puzzle
* : Answers: $269$. A Triangle Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/204 - The Donjon Keep Window

== by : $204$ ==
;The Donjon Keep Window
:In Sir Hugh de Fortibus calls his chief builder, and, pointing to a window, says:
::"Methinks yon window is square, and measures, on the inside, one foot every way,
::and is divided by the narrow bars into four lights, measuring half a foot on every side."
:See our Figure $A$.
:"I desire that another window be made higher up,
::whose four sides shall also be each one foot,
::but it shall be divided by bars into eight lights, whose sides shall be all equal."
:This the craftsman was unable to do, so Sir Hugh showed him our Figure $B$, which is quite correct.
:
:But he added, "I did not tell thee that the window must be square, as it is most certain it never could be."
:Now, an ingenious correspondent, Mr. George Plant, found a flaw in Sir Hugh's conditions.
:Something that was understood is not actually stated,
::and the window may, as the conditions stand, be perfectly square.
:How is it to be done?
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $204$. -- The Donjon Keep Window
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $270$. The Donjon Keep Window
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/204 - The Donjon Keep Window/Solution

== by : $204$ ==
;The Donjon Keep Window
== Solution ==
Every side of every light of this window is of the same length.
:
It was never said that the lights should all be the same area.
The irregular lights are in fact $25\%$ larger than the square ones.
== Sources ==
* : Solutions: $204$. -- The Donjon Keep Window
* : Answers: $270$. The Donjon Keep Window
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/205 - The Square Window

== by : $205$ ==
;The Square Window
:A man had a window a yard square, and it let in too much light.
:He blocked up one half of it, and still had a square window a yard high and a yard wide.
:How did he do it??
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $205$. -- The Square Window
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $271$. The Square Window
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/205 - The Square Window/Solution

== by : $205$ ==
;The Square Window
== Solution ==
The shaded areas are the bits he blocked in.
:
== Sources ==
* : Solutions: $205$. -- The Square Window
* : Answers: $271$. The Square Window
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/206 - The Triangular Plantation

== by : $206$ ==
;The Triangular Plantation
:A man had a plantation of twenty-one trees set out in the triangular form shown in the diagram.
:
:If he wished to enclose a triangular piece of ground with a tree at each of the three angles,
::how may different ways of doing it are there from which he might select?
:The dotted lines show three ways of doing it.
:How many are there altogether?
:This is just one of those puzzles that call for the exercise of a little cunning in the solving.
=== Click here for solution ===
== Sources ==
* : Geometrical Problems: Various Geometrical Puzzles: $206$. -- The Triangular Plantation
* : Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $286$. The Triangular Plantation
Category:Henry Ernest Dudeney/Puzzles and Curious Problems