Combinatorics · Tournaments · Directed graphs · Hamiltonian path · Redei theorem
At a volleyball tournament \(n > 1\) teams took part, and every two of them played exactly one match against each other. Prove that the teams can be numbered \(1, 2, \ldots, n\) in such a way that for every \(i \in \{1, 2, \ldots, n-1\}\) the team numbered \(i\) beat the team numbered \(i+1\) in their mutual match.
(A volleyball match cannot end in a draw.)
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Serbian Regional Competition (Okruzno takmicenje) 2013, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source