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  • $\begingroup$ Great! I had a feeling there was a more direct approach but I could not see my way to it. I knew I needed a way to "contract" the distance between points joined by existing lines but I struggled to do it. Treating odd indices seems obvious now but it was not at the time, like so many great ideas. $\endgroup$ Commented Jan 26, 2017 at 5:23
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    $\begingroup$ I'm probably having another moment of obtuseness but why can one not use dist[a_?OddQ, b_] /; (b == a + 1) := 0? $\endgroup$ Commented Jan 26, 2017 at 6:16
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    $\begingroup$ There is one issue with this as written: the order always starts with {1} whereas in practice it should start with one of the ends, i.e. {9} or {33}. $\endgroup$ Commented Jan 26, 2017 at 7:29
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    $\begingroup$ To handle adjacent line segments that start and end on the same point I needed to add a constant to the distance, e.g. dist[a_, b_] := 1 + EuclideanDistance[d[[a]], d[[b]]] $\endgroup$ Commented Jan 26, 2017 at 7:54
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    $\begingroup$ @Mr.Wizard, you can use zero distance. An earlier attempt did not work with zero as it allowed lines to be traversed multiple times in both directions. I hadn't realised that my workaround was no longer necessary. The start point is a problem. FindShortestTour identifies a complete circuit so it could perhaps be post-processed to split at the largest gap. $\endgroup$ Commented Jan 26, 2017 at 19:46