Combinatorics · Graphs · Eulerian circuits · Cut vertex · Counterexamples
Baron Munchausen lives in a country \(Z\) which has \(2018\) cities, some pairs of them joined by roads (every road can be travelled in both directions). The Baron has established that there is a city \(A\) from which one can set out on a journey, travel along every road of the country exactly once, and come back to \(A\).
He claims that it follows from this that for any two roads \(p\) and \(r\) leaving one and the same city there is a journey, starting from some city \(B\) and ending at \(B\), which passes along every road exactly once and traverses the roads \(p\) and \(r\) immediately one after the other. Is he right, or is he lying as usual?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Municipal Competition 2018, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source