THE UNION JACK.
(
Unicursal and Route Problems)
The illustration is a rough sketch somewhat resembling the British flag,
the Union Jack. It is not possible to draw the whole of it without
lifting the pencil from the paper or going over the same line twice. The
puzzle is to find out just _how much_ of the drawing it is possible to
make without lifting your pencil or going twice over the same line. Take
your pencil and see what is the best you can do.
Answer:
[Illustration:
+-------+ +-----
A B | | /
| | /
| | | / /|
| | | / / |
| | |/ / |
| | / / |
| | /| / |
+------|-/-|-/-----+
| / |/
|/ /
| /
/| / |
+-----/-|-/-|------+
| / / | |
| / | |
| / /| | |
| / / | | |
|/ / | | |
/ | |
/ | |
-----+ +-----
]
There are just sixteen points (all on the outside) where three roads may
be said to join. These are called by mathematicians "odd nodes." There
is a rule that tells us that in the case of a drawing like the present
one, where there are sixteen odd nodes, it requires eight separate
strokes or routes (that is, half as many as there are odd nodes) to
complete it. As we have to produce as much as possible with only one of
these eight strokes, it is clearly necessary to contrive that the seven
strokes from odd node to odd node shall be as short as possible. Start
at A and end at B, or go the reverse way.
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