Henry Ernest Dudeney/Puzzles and Curious Problems/Unicursal and Route Problems

Henry Ernest Dudeney: Puzzles and Curious Problems: Unicursal and Route Problems

$261$ - The Twenty-Two Bridges

We have a rough map of a district with an elaborate system of irrigation,

as the various waterways and numerous bridges will show.

A man set out from one of the lettered departments to pay a visit to a friend living in a different department.

For the purpose of pedestrian exercise he crossed every one of the bridges once, and once only.

The puzzle is to show in which two departments their houses are situated.

$262$ - A Monmouth Tombstone

In the burial ground attached to St. Mary's Church, Monmouth, is this arrangement of letters on one of the tombstones.

$\qquad \begin{array} \\ E & I & N & E & R & N & H & O & J & S & J & O & H & N & R & E & N & I & E \\ I & N & E & R & N & H & O & J & S & E & S & J & O & H & N & R & E & N & I \\ N & E & R & N & H & O & J & S & E & I & E & S & J & O & H & N & R & E & N \\ E & R & N & H & O & J & S & E & I & L & I & E & S & J & O & H & N & R & E \\ R & N & H & O & J & S & E & I & L & E & L & I & E & S & J & O & H & N & R \\ N & H & O & J & S & E & I & L & E & R & E & L & I & E & S & J & O & H & N \\ H & O & J & S & E & I & L & E & R & E & R & E & L & I & E & S & J & O & H \\ O & J & S & E & I & L & E & R & E & \mathbf H & E & R & E & L & I & E & S & J & O \\ H & O & J & S & E & I & L & E & R & E & R & E & L & I & E & S & J & O & H \\ N & H & O & J & S & E & I & L & E & R & E & L & I & E & S & J & O & H & N \\ R & N & H & O & J & S & E & I & L & E & L & I & E & S & J & O & H & N & R \\ E & R & N & H & O & J & S & E & I & L & I & E & S & J & O & H & N & R & E \\ N & E & R & N & H & O & J & S & E & I & E & S & J & O & H & N & R & E & N \\ I & N & E & R & N & H & O & J & S & E & S & J & O & H & N & R & E & N & I \\ E & I & N & E & R & N & H & O & J & S & J & O & H & N & R & E & N & I & E \\ \end{array}$

In how many different ways can these words "$\text{HERE LIES JOHN RENIE}$" be read,

starting at the central $H$ and always passing from one letter to another that is contiguous?

$263$ - Footprints in the Snow

Four schoolboys, living respectively in the houses $A$, $B$, $C$, and $D$, attended different schools.

After a snowstorm one morning their footprints were examined, and it was found that no boy had ever crossed the track of another boy,

or gone outside the square boundary.

Take your pencil and continue their tracks, so that the boy $A$ goes to the school $A$, the boy $B$ to the school $B$, and so on,

without any line crossing another line.

$264$ - The Fly's Tour

A fly pitched on the square in the top left-hand corner of a chessboard,

and then proceeded to visit every white square.

He did this without ever entering a black square or ever passing through the same corner more than once.

Can you show his route?

It can be done in seventeen continuous straight courses.

$265$ - Inspecting the Roads

A man starting from the town $A$, has to inspect throughout all the roads shown from town to town.

Their respective lengths, $13$, $12$, and $5$ miles, are all shown.

What is the shortest route he can adopt, ending his journey wherever he likes?

$266$ - Railway Routes

The diagram below represents a simplified railway system,

and we want to know how many different ways there are of going from $A$ to $E$, if we never go twice along the same line in any journey.

$267$ - A Motor-Car Tour

A man started in a motor-car from town $A$, and wished to make a complete tour of these roads,

going along every one of them once, and once only.

How many different routes are there from which he can select?

Every route must end at the town $A$, from which you start,

and you must go straight from town to town -- never turning off at crossroads.

$268$ - Mrs. Simper's Holiday Tour

The diagram shows a plan, very much simplified, of a tour that Mrs. Simper proposes to take next autumn.

It will be seen that there are $20$ towns, all connected by railway lines.

Mrs. Simper lives at $H$, and wants to visit every other town once and once only, ending her tour at home.

There are in fact $60$ possible routes she can select from, counting the reverse of a route as different.

There is a tunnel between $N$ and $O$, and one between $R$ and $S$, but Mrs. Simper does not want to go through these.

She also wants to delay her visit to $D$ as long as possible so as to meet a friend who lives there.

The puzzle is to show Mrs. Simper the best route under these circumstances.

$269$ - Sixteen Straight Runs

A commercial traveller started in his car from the point $A$ shown,

and wished to go $76$ miles in $16$ straight runs, never going along the same road twice.

The dots represent the towns and villages, and these are one mile apart.

The lines show the route he selected.

It will be seen that he carried out his plan correctly, but $6$ towns or villages were unvisited.

Can you show a better route by which he could have gone $76$ miles in $16$ straight runs, and left only $3$ towns unvisited?

$270$ - Planning Tours

The diagram represents a map (considerably simplified for our purposes) of a certain district.

The circles and dots are towns and villages, and the lines roads.

Can you show how $5$ motor-car drivers can go from $A$ to $A$, from $B$ to $B$, from $C$ to $C$, from $D$ to $D$, from $E$ to $E$, respectively,

without ever crossing the track or going along the same road as another car?

$271$ - Avoiding the Mines

Here we have a portion of the North Sea thickly sown with mines by the enemy.

A cruiser made a safe passage through them from south to north in two straight courses, without striking a single mine.

Take your pencil and try to discover how it is done.

Go from the bottom of the chart to any point you like on the chart in a straight line,

and then from that point to the top in another straight line without touching a mine.

$272$ - A Madam Problem

In how many different ways is it possible to read the word $\text {MADAM}$ in the diagram?

You may go as you please, upwards and downwards, forwards and backwards,

any way possible along the open paths.

But the letters in every case must be contiguous, and you may never pass a letter without using it.