Combinatorics · Round robin tournament · Double counting · Integer inequalities
Problem 5, 2002
In a handball tournament every team played exactly one match against each of the other teams. A win is worth \(2\) points, a loss \(0\), and a drawn match gives \(1\) point to each of the two teams. The three best placed teams scored \(7\), \(5\) and \(3\) points. How many teams took part in the tournament, and how many points did the last placed team score? (Teams with equally many points are ordered by goal difference.)
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Serbian Municipal Competition 2002, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source