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The shortest road network
Contributed by Josh, July 19, 2000 and originally answered by Valerio De Angelis
Four towns are located at the vertices of a 4 mile by 6 mile rectangle. By using three sides of the rectangle, a road network of total length 14 miles can be constructed which connects all four towns. Is there a shorter road network, which connects the towns? Specifically, there is a suitable network of length less that 13 miles.