Henry Ernest Dudeney/Modern Puzzles/155 - Marking a Tennis Court/Solution

Modern Puzzles by Henry Ernest Dudeney: $155$

The lines of our tennis court are faint and want re-marking.

My marker is of such a kind that, though I can start anywhere and finish anywhere,

it cannot be lifted off the line when working without making a mess.

I therefore have to go over some of the lines twice.

Where should I start and what route should I take, without lifting the marker,

to mark the court completely and yet go over the minimum distance twice?

I give the correct proportions of a tennis court in feet.

What is the best route?

The $10$ labelled points are vertices of degree $3$, and therefore odd.

Hence we need to run over at least $4$ lines twice.

The shortest possible double tracking is running $BE$, $CD$, $GH$ and $FJ$ twice.

Hence the route to take:

$ADCDKGHGABEBCFJFEHK$

or its reverse.

There are minor variants:

By symmetry, $EH$, $AB$, $CF$ and $JK$ could be the lines to double track, then we start at $G$ and end at $D$, or the other way about

We could run over the double-tracked lines when we encounter the other end of them when we reach them, for example: $ADKGABCDCFEBEHGHJFJK$

and so on.

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $155$. -- Marking a Tennis Court
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $412$. Marking a Tennis Court