Combinatorics · Arrangements of lines · Counting regions · Incremental counting · General position · Optimization with fixed sum
In the plane of a triangle \(ABC\) one draws \(n\) lines, each of them parallel to one of the three sides of the triangle. Determine the smallest \(n\) for which these \(n\) lines can cut the plane into at least \(207\) regions, counting the unbounded regions along with the bounded ones.
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Serbian National Competition (Drzavno takmicenje) 2007, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source