Enigma 108: Longest journey
16 July 2013
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From New Scientist #1252, 7th May 1981 [link]
Here we have uniform square grid of roads, each 6 miles long, intersecting at 49 junctions. I want a route, starting at any junction and ending at any junction, and not going twice along any stretch of road, which meets two requirements: (1) It is as long as possible; (2) subject to that, it consists of as few “legs” as possible. In addition I should prefer a route which includes every junction, if that is possible without making the route shorter or leggier.
How many miles, and how few legs, in a route which best meets my requirements and my preferences?