nyuuzyou/wikis huggingface dataset:
Henry Ernest Dudeney/Puzzles and Curious Problems/249 - Odds and Evens/Solution

== by : $249$ ==
;Odds and Evens
== Solution ==
The fewest possible moves are as follows, given by ordered pairs of the letters identifying the circles from and to which the counters are moved.
:$\tuple {E, A}, \tuple {E, B}, \tuple {E, C}, \tuple {E, D}, \tuple {B, D}, \tuple {E, B},$
:$\tuple {C, B}, \tuple {A, B}, \tuple {E, C}, \tuple {E, A}, \tuple {B, A}, \tuple {C, E},$
:$\tuple {B, C}, \tuple {A, C}, \tuple {B, A}, \tuple {C, B}, \tuple {C, A}, \tuple {B, A},$
:$\tuple {E, C}, \tuple {E, B}, \tuple {C, B}, \tuple {D, E}, \tuple {D, B}, \tuple {E, B}$
That is, $24$ moves.
== Sources ==
* : Solutions: $249$. -- Odds and Evens
* : Answers: $373$. Odds and Evens
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/24 - The Two Turkeys

== by : $24$ ==
;The Two Turkeys
:"I sold those two turkeys," said Tozer.
:"They weighed $20$ pounds together.
:Mrs. Burkett paid $24 \shillings 8 \oldpence$ for the large one, and Mrs. Suggs paid $6 \shillings 10 \oldpence$ for the small one.
:I made $2 \oldpence$ a pound more on the little one than on the other."
:What did the big one weigh?
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $24$. -- The Two Turkeys
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/24 - The Two Turkeys/Solution

== by : $24$ ==
;The Two Turkeys
== Solution ==
:$16$ pounds.
== Proof ==
Let $L$ and $S$ pounds be the weight of the large and small turkeys together.
Let all prices be considered in pence in order to reduce the need to handle fractions.
The price in pence per pound for the large turkey is:
:$\dfrac {24 \times 12 + 8} L = \dfrac {296} L$
The price in pence per pound for the large turkey is:
:$\dfrac {6 \times 12 + 10} S = \dfrac {82} S$
We have:
Only the positive root is required here.
Hence the result.
== Sources ==
* : Solutions: $24$. -- The Two Turkeys
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/250 - Adjusting the Counters

== by : $250$ ==
;Adjusting the Counters
:Place $25$ counters in a square in the order shown.
:
:Then it is a good puzzle to put them all into regular order so that the first line reads $1 \ 2 \ 3 \ 4 \ 5$, and the second $6 \ 7 \ 8 \ 9 \ 10$,
::and so on to the end, by taking up one counter in each hand and making them change places.
:The puzzle is to determine the fewest possible exchanges in which this can be done.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $250$. -- Adjusting the Counters
* : Geometrical Problems: Moving Counter Puzzles: $375$. Adjusting the Counters
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/250 - Adjusting the Counters/Solution

== by : $250$ ==
;Adjusting the Counters
== Solution ==
The task can be accomplished in $19$ exchanges:
:$(1): \quad \tuple {1, 7}, \tuple {7, 20}, \tuple {20, 16}, \tuple {16, 11}, \tuple {11, 2} \tuple {2, 24}$
:$(2): \quad \tuple {3, 10}, \tuple {10, 23}, \tuple {23, 14}, \tuple {14, 18}, \tuple {18, 5}$
:$(3): \quad \tuple {4, 19}, \tuple {19, 9}, \tuple {9, 22}$
:$(4): \quad \tuple {6, 12}, \tuple {12, 15}, \tuple {15, 13}, \tuple {13, 25}$
:$(5): \quad \tuple {17, 21}$
== Proof ==
First we identify the permutation required to perform the operation.
We present it in two-row notation as follows
:$\begin{pmatrix}
7 & 24 & 10 & 19 & 3 & 12 & 20 & 8 & 22 & 23 & 2 & 15 & 25 & 18 & 13 & 11 & 21 & 5 & 9 & 16 & 17 & 4 & 14 & 1 & 6 \\
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 \end{pmatrix}$
From this we can identify the cycles and hence present it in cycle notation:
:$\begin{pmatrix} 1 & 7 & 20 & 16 & 11 & 2 & 24 \end{pmatrix}
\begin{pmatrix} 3 & 10 & 23 & 14 & 18 & 5 \end{pmatrix}
\begin{pmatrix} 4 & 19 & 9 & 22 \end{pmatrix}
\begin{pmatrix} 6 & 12 & 15 & 13 & 25 \end{pmatrix}
\begin{pmatrix} 17 & 21 \end{pmatrix}$
Then it is seen that the exchanges should be done as:
:$(1): \quad \tuple {1, 7}, \tuple {7, 20}, \tuple {20, 16}, \tuple {16, 11}, \tuple {11, 2} \tuple {2, 24}$
:$(2): \quad \tuple {3, 10}, \tuple {10, 23}, \tuple {23, 14}, \tuple {14, 18}, \tuple {18, 5}$
:$(3): \quad \tuple {4, 19}, \tuple {19, 9}, \tuple {9, 22}$
:$(4): \quad \tuple {6, 12}, \tuple {12, 15}, \tuple {15, 13}, \tuple {13, 25}$
:$(5): \quad \tuple {17, 21}$
The squareness of the array of numbers to be arranged is irrelevant.
== Sources ==
* : Solutions: $250$. -- Adjusting the Counters
* : Answers: $375$. Adjusting the Counters
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/251 - Nine Men in a Trench

== by : $251$ ==
;Nine Men in a Trench
:Here are nine men in a trench.
:
:No. $1$ is the sergeant, who wishes to place himself at the other end of the line -- at point $1$ --
::all the other men returning to their proper places at present.
:There is no room to pass in the trench, and for a man to climb over another would be a dangerous exposure.
:But it is not difficult with these three recesses, each of which will hold a man.
:How is it to be done with the fewest possible moves?
:A man may go any distance that is possible in a move.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $251$. -- Nine Men in a Trench
* : Geometrical Problems: Moving Counter Puzzles: $376$. Nine Men in a Trench
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/251 - Nine Men in a Trench/Solution

== by : $251$ ==
;Nine Men in a Trench
:Here are nine men in a trench.
:
:No. $1$ is the sergeant, who wishes to place himself at the other end of the line -- at point $1$ --
::all the other men returning to their proper places at present.
:There is no room to pass in the trench, and for a man to climb over another would be a dangerous exposure.
:But it is not difficult with these three recesses, each of which will hold a man.
:How is it to be done with the fewest possible moves?
:A man may go any distance that is possible in a move.
== Solution ==
Move the men in the following order:
:$2 - 1$, $3 - 2$, $4 - 3$, $5 - 11$, $6 - 4$, $7 - 5$, $8 - 6$,
:$9 - 7$, $1 - 13$, $9 - 10$, $8 - 9$, $1 - 12$, $7 - 13$, $6 - 8$
:$5 - 7$, $1 - 11$, $4 - 12$, $3 - 6$, $2 - 5$, $1 - 1$, $2 - 2$
:$3 - 3$, $4 - 4$, $5 - 5$, $6 - 6$, $7 - 7$, $8 - 8$, $9 - 9$
and the sergeant is in his place in $28$ moves.
== Sources ==
* : Solutions: $251$. -- Nine Men in a Trench
* : Answers: $376$. Nine Men in a Trench
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/252 - Black and White

== by : $252$ ==
;Black and White
:Place four light and four dark counters alternately in a row as here shown.
:
:The puzzle is to transfer two contiguous counters to one end and then move two contiguous counters to the vacant space,
::and so on until in four such moves they form a continuous line of four dark counters followed by four light ones.
:Then try this variant.
:The conditions are exactly the same, only in moving a contiguous pair you must make them change sides.
:How many moves do you now require?
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $252$. -- Black and White
* : Geometrical Problems: Moving Counter Puzzles: $377$. Black and White
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/252 - Black and White/Solution

== by : $252$ ==
;Black and White
== Solution ==
:$(1): \quad$ In the first case, move:
:::$6 7$ before the $1$, then $3 4$, $7 1$, $4 8$ to the vacant spaces, leaving the order:
::::$6 \ 4 \ 8 \ 2 \ 7 \ 1 \ 5 \ 3$
:$(2): \quad$ In the second case, move:
:::$3 4$ and replace them as $4 3$ before the $1$, then move and reverse $6 7$, $6 5$, $3 1$, $6 8$ into the vacant spaces, leaving the order:
::::$4 \ 8 \ 6 \ 2 \ 7 \ 1 \ 3 \ 5$
== Sources ==
* : Solutions: $252$. -- Black and White
* : Answers: $377$. Black and White
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle

== by : $253$ ==
;The Angelica Puzzle
:Draw a square with three lines in both direction and place on the intersecting points eight lettered counters as shown in our illustration.
:
:The puzzle is to move the counters, one at a time, along the lines from point to vacant point until you get them in the order $\text {ANGELICA}$ thus:
::$\begin{array} \\ A & N & G \\ E & L & I \\ C & A & .\end {array}$
:Try to do this in the fewest possible moves.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $253$. -- The Angelica Puzzle
* : Geometrical Problems: Moving Counter Puzzles: $378$. The Angelica Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle
Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Historical Note

== Historical Note on by : $253$ - The Angelica Puzzle ==
The original solution found by was of $36$ moves.
 reported on a $30$-move solution, but left it as an exercise for the reader to find.
== Sources ==
* : Answers: $378$. The Angelica Puzzle
Category:Historical Notes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle
Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution

== by : $253$ ==
;The Angelica Puzzle
== Solution ==
:Though we start with the $A$s in the correct positions, the puzzle can only be solved by making them change places.
:Representing the $A$ in the bottom row with a capital, and the $A$ in the top corner with a small letter, the moves are as follows:
=== Solution $1$ ===
=== Solution $2$ ===
== Historical Note ==
== Sources ==
* : Solutions: $253$. -- The Angelica Puzzle
* : Answers: $378$. The Angelica Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle
Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution 1

== by : $253$ ==
;The Angelica Puzzle
== Solution ==
:Though we start with the $A$s in the correct positions, the puzzle can only be solved by making them change places.
:Representing the $A$ in the bottom row with a capital, and the $A$ in the top corner with a small letter, the moves are as follows:
:$A \ N \ L \ E \ G \ A \ N \ G \ C \ I \ A \ N \ G \ C \ I \ A \ N \ G \ C \ L \ E \ a \ A \ N \ G \ I \ L \ C \ I \ L \ a \ E \ C \ a \ L \ I$
:which is $36$ moves in all.
== Historical Note ==
== Sources ==
* : Solutions: $253$. -- The Angelica Puzzle
* : Answers: $378$. The Angelica Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle
Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution 2

== by : $253$ ==
;The Angelica Puzzle
== Solution ==
:Though we start with the $A$s in the correct positions, the puzzle can only be solved by making them change places.
:Representing the $A$ in the bottom row with a capital, and the $A$ in the top corner with a small letter, the moves are as follows:
:$\texttt {G E C a L N A C a L N A C a L I E G a L I E G I E N A E L a}$
:which is $30$ moves in all.
There are $9$ more solutions with $30$ moves:
:$\texttt {G E C a L N A C E G C E a I G a I L N A E C a I L N A E C a}$
:$\texttt {G E L a C L A G E I L A G N a C A G N E I L G N E a C E L I}$
:$\texttt {G E L N A L C I E G L C I a N A C I a E G L I a E N A E L I}$
:$\texttt {G E L N A L E G L E C a N A E C a I G a I N A E C L a I L a}$
:$\texttt {A E C a L N E C a I G a I L N E C A a I A C E A L N A E C a}$
:$\texttt {A E G A E N L a C G A I G A N L a C A N L E I L E a C E L I}$
:$\texttt {A E L a C L G I L G E A I L G E A N a C E A N a C E A N L I}$
:$\texttt {A N L a C E G A N L a C E G A I G A L N I L N a C E A N L I}$
:$\texttt {A N L a C E a L N a G A a N L C E G A I G A N L C E A N L a}$
== Historical Note ==
== Sources ==
* : Answers: $378$. The Angelica Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel

== by : $254$ ==
;The Flanders Wheel
:Place eight lettered counters on the wheel as shown.
:
:Now move them one at a time along the line from circle to circle
::until the word $\text {FLANDERS}$ can be correctly read round the rim of the wheel as at present,
::only that the $\text F$ is in the upper circle now occupied by the $\text N$.
:Of course two counters cannot be in a circle at the same time.
:Find the fewest possible moves.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $254$. -- The Flanders Wheel
* : Geometrical Problems: Moving Counter Puzzles: $379$. The Flanders Wheel
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Historical Note

== Historical Note on by : $254$ - The Flanders Wheel ==
The $30$-move solution was that given by .
The $28$-move solution was reported on by , who set it as a puzzle for his readers to solve.
He notes that it is isomorphic with a sliding-block puzzle of $8$ blocks on a $3 \times 3$ square array.
He then references his Mathematical Games columns in for March and June $1965$.
== Sources ==
* : Answers: $379$. The Flanders Wheel
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Category:Historical Notes
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution

== by : $254$ ==
;The Flanders Wheel
== Solution ==
=== Solution $1$ ===
=== Solution $2$ ===
== Historical Note ==
== Sources ==
* : Solutions: $254$. -- The Flanders Wheel
* : Answers: $379$. The Flanders Wheel
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution/Mistake

== Source Work ==
:
:Moving Counter Problems
::$254$ -- The Flanders Wheel
== Mistake ==
:Move the counters in the following order: $\text {A N D A F L N D A F D N L D R S D L N A F R S E R S L N A L L}$ -- $30$ moves in all.
There is an extra $\text L$ at the end.
The list of moves should read:
:$\text {A N D A F L N D A F D N L D R S D L N A F R S E R S L N A L}$
This mistake has been corrected in 's republication of this as puzzle $379$ in .
== Sources ==
* : Solutions: $254$. -- The Flanders Wheel
Category:Mistakes/Puzzles and Curious Problems
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution 1

== by : $254$ ==
;The Flanders Wheel
== Solution ==
Move the counters in the following order:
:$\texttt {A N D A F L N D A F D N L D R S D L N A F R S E R S L N A L}$
which is $30$ moves in all.
== Historical Note ==
== Sources ==
* : Solutions: $254$. -- The Flanders Wheel
* : Answers: $379$. The Flanders Wheel
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution 2

== by : $254$ ==
;The Flanders Wheel
== Solution ==
Move the counters in this order:
:$\texttt {D N A D R E N R F S E N R F S L D A F S L D A L N E D N}$
or this order:
:$\texttt {F S R F A L S A D N L S A D N E F R D N E F R E S L F S}$
which are both $28$ moves in all.
== Historical Note ==
== Sources ==
* : Answers: $379$. The Flanders Wheel
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel
Henry Ernest Dudeney/Puzzles and Curious Problems/255 - A Peg Puzzle

== by : $255$ ==
;A Peg Puzzle
:The diagram represents a square board with $49$ holes in it.
:There are $10$ pegs to be placed in the positions shown,
::and the puzzle is to remove only $3$ of these pegs to different holes,
::so that the ten shall form $5$ rows with $4$ pegs in every row.
:
:Which three would you move, and where would you place them?
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $255$. -- A Peg Puzzle
* : Combinatorial & Topological Problems: Point Alignment Puzzles: $438$. A Peg Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/255 - A Peg Puzzle/Solution

== by : $255$ ==
;A Peg Puzzle
== Solution ==
The crosses indicate where the pegs were moved from.
:
== Also see ==
* $257$ - Five Lines of Four in this collection, practically the same puzzle as this one.
* $258$ - Deploying Battleships in this collection, another similar take.
== Sources ==
* : Solutions: $255$. -- A Peg Puzzle
* : Answers: $438$. A Peg Puzzle
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/256 - Catching the Prisoners

== by : $256$ ==
;Catching the Prisoners
:Make a rough diagram on a sheet of paper, and use counters to indicate the two warders (marked as $W$) and the two prisoners (marked as $P$).
:
:At the beginning the counters must be placed in the squares shown.
:The first player moves each of the warders to an adjacent cell, in any direction.
:Then the second player moves each prisoner to an adjoining cell;
::and so on until each warder captures his prisoner.
:If one warder makes a capture, both he and his captive are out of the game, and the other player continues alone.
:You may come to the conclusion that it is a hopeless chase, but it can really be done if you use a little cunning.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $256$. -- Catching the Prisoners
* : Geometrical Problems: Moving Counter Puzzles: $380$. Catching the Prisoners
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/256 - Catching the Prisoners/Solution

== by : $256$ ==
;Catching the Prisoners
== Solution ==
The trick is that it is impossible for the warder to catch the nearer prisoner.
He has to aim for the one on the opposite side of the prison.
Let the squares be labelled $1$ to $40$, reading across then down.
Let the prisoners and warders be labelled $P_1$, $P_2$, $W_1$ and $W_2$ as shown.
:
Then we present a specimen game, where the warders' moves are above the line, the prisoners's below.
:$\dfrac {19-20 \ 22-14} {17-18 \ 24-23}, \dfrac {20-21 \ 14-13} {18-26 \ 23-31}, \dfrac {21-22 \ 13-12} {26-27 \ 31-32}, \dfrac {22-23 \ 12-20} {27-26 \ 32-40}, \dfrac {23-31 \ 20-19} {40-32 \ 26-34}, \dfrac {31-32 \text { Capture} \ 19-27} {\qquad \qquad \qquad \ 34-33}, \dfrac {27-26} {33-25}, 26-25 \text { Capture}$
== Sources ==
* : Solutions: $256$. -- Catching the Prisoners
* : Answers: $380$. Catching the Prisoners
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/257 - Five Lines of Four

== by : $257$ ==
;Five Lines of Four
:The diagram shows how ten counters may be placed on the points of the grid where the lines intersect,
::so that they form five straight lines with four counters in every line.
:
:Can you find a second way of doing this?
:Of course a mere reversal or reflection of the given arrangement is not considered different --
::it must be a new scheme altogether, and of course you cannot increase the dimensions of the diagram or alter its shape.
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $257$. -- Five Lines of Four
* : Combinatorial & Topological Problems: Point Alignment Puzzles: $439$. Five Lines of Four
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/257 - Five Lines of Four/Solution

== by : $257$ ==
;Five Lines of Four
== Solution ==
:
== Also see ==
* $255$ - A Peg Puzzle in this collection, practically the same puzzle as this one.
* $258$ - Deploying Battleships in this collection, another similar take.
== Sources ==
* : Solutions: $257$. -- Five Lines of Four
* : Answers: $439$. Five Lines of Four
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/258 - Deploying Battleships

== by : $258$ ==
;Deploying Battleships
:Ten battleships were anchored in the form here shown.
:
:The puzzle is for four ships to move to new positions (the others remaining where they are)
::until the ten form five straight rows with four ships in each row.
:How should the admiral do it?
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $258$. -- Deploying Battleships
* : Combinatorial & Topological Problems: Point Alignment Puzzles: $440$. Deploying Battleships
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/258 - Deploying Battleships/Solution

== by : $258$ ==
;Deploying Battleships
== Solution ==
The white dots indicate where the ships were moved from.
The black dots indicate where they were moved to.
The blue dots indicate ships that did not move.
:
== Also see ==
* $255$ - A Peg Puzzle and $257$ - Five Lines of Four, both similar to this.
== Sources ==
* : Solution: $258$. -- Deploying Battleships
* : Answers: $440$. Deploying Battleships
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/259 - Flies on Window Panes

== by : $259$ ==
;Flies on Window Panes
:The diagram represents a window with $81$ panes.
:The dots represent nine flies, on as many panes,
::and no fly is in line with another one horizontally, vertically, or diagonally.
:
:Six of those flies are very torpid and do not move,
::but each of the remaining three goes to an adjoining pane.
:And yet, after this change of station, no fly is in line with another.
:Which are the three lively flies, and to which three panes (at present unoccupied), do they pass?
=== Click here for solution ===
== Sources ==
* : Moving Counter Problems: $259$. -- Flies on Window Panes
* : Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $456$. Flies on Window Panes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/259 - Flies on Window Panes/Solution

== by : $259$ ==
;Flies on Window Panes
== Solution ==
The arrows show which flies have moved.
:
== Sources ==
* : Solution: $259$. -- Flies on Window Panes
* : Answers: $456$. Flies on Window Panes
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions
Henry Ernest Dudeney/Puzzles and Curious Problems/25 - Flooring Figures

== by : $25$ ==
;Flooring Figures
:A correspondent accidentally discovered the following when making out an invoice with the items:
::$148 \ \mathrm {ft.}$ flooring boards at $2 \oldpence$ $\pounds 1, 4 \shillings 8 \oldpence$
::$150 \ \mathrm {ft.}$ flooring boards at $2 \oldpence$ $\pounds 1, 5 \shillings 0 \oldpence$
:where it will be seen that in each case the three digits are repeated in the same order.
:He thought this coincidence so extraordinary that he tried to find another similar case.
:This seems to have floored him. But it is possible.
:You may increase the number of pence if you like, but not use fractions of a penny.
=== Click here for solution ===
== Sources ==
* : Arithmetical and Algebraical Problems: Money Puzzles: $25$. -- Flooring Figures
Category:Henry Ernest Dudeney/Puzzles and Curious Problems
Henry Ernest Dudeney/Puzzles and Curious Problems/25 - Flooring Figures/Solution

== by : $25$ ==
;Flooring Figures
== Solution ==
The only other answer appears to be:
:$298 \ \mathrm {ft.}$ flooring boards at $2 \oldpence = \pounds 2, 9 \shillings 8 \oldpence$
== Sources ==
* : Solutions: $25$. -- Flooring Figures
Category:Henry Ernest Dudeney/Puzzles and Curious Problems/Solutions