Every street in Hamiltonville connects two squares
Source: Tuymaada 2008, Senior League, Second Day, Problem 5.
July 20, 2008
graph theorycombinatorics unsolvedcombinatorics
Problem Statement
Every street in the city of Hamiltonville connects two squares, and every square may be reached by streets from every other. The governor discovered that if he closed all squares of any route not passing any square more than once, every remained square would be reachable from each other. Prove that there exists a circular route passing every square of the city exactly once.
Author: S. Berlov