Combinatorics · Line arrangements · Parallel classes · Counting
Several lines are drawn in the plane. Line \(a\) intersects exactly three of the other lines, and line \(b\) intersects exactly four of the other lines. Line \(c\) intersects exactly \(n\) of the other lines, where \(n \ne 3\) and \(n \ne 4\).
How many lines are drawn in the plane?
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Serbian Municipal Competition 2015, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source