I believe that what you have described is the "Travelling Salesman Problem", not the Euler problem. TSP is the Fedex/UPS/Amazon(?) delivery problem. Euler problem is easily solveable (whether possible), TSP is NP-hard. https://en.wikipedia.org/wiki/Travelling_salesman_problem https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg BTW, I've never seen a mathematical characterization of what I call the "bicycle touring problem": the problem of riding for N miles on the most pleasant roads possible without repeats (or without significant repeats). The focus is on _links_, not _nodes_, and we want to maximize the pleasantness of the total trip, or perhaps minimize the maximum unpleasantness of the worst link. The BTP may be closer to the Euler problem than the TSP. At 11:36 AM 6/4/2014, Thane Plambeck wrote:

I thought this was interesting...a Google map allegedly showing how to drive a car through the lower 48 USA states, visiting each state [at least? exactly?] once and minimizing the total distance travelled.

http://goo.gl/maps/90i0Y

-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/