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My first instinct is to have the salesman criss-cross as much as possible. The route I would take (just a guess, haven't verified) is 1, 5, 2, 6, 3, 8, 4, 7 for a total of 41.989 units traveled.

BG has the longest (non-returning) path.

I have marked the puzzle solved, but we still have the longest (closed-loop) path to determine.

(Post solutions in terms of the corrected 7-8 numbering and corrected 6.325 distance.)

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution. - Bertrand Russell

I'm not sure which order of 7 and 8 you are using, but I see one path that is too short to use.

There are no (chess) Knight moves, like 7-5 and 2-8 (using the correct 7 8 labeling).

If you are using the original 8 7 labeling you are not using knight moves, but too many 1-4 type moves.

Clue for those still working on this the longest total length is 47.97, and from that you can get the distribution of city-city distances used, and work out the path.

Try my next, harder puzzle just posted.

0

The greatest challenge to any thinker is stating the problem in a way that will allow a solution. - Bertrand Russell

I'm not sure which order of 7 and 8 you are using, but I see one path that is too short to use.

There are no (chess) Knight moves, like 7-5 and 2-8 (using the correct 7 8 labeling).

If you are using the original 8 7 labeling you are not using knight moves, but too many 1-4 type moves.

Clue for those still working on this the longest total length is 47.97, and from that you can get the distribution of city-city distances used, and work out the path.