# Combinatorics in geometry

Geometry Level 4

We draw $$2017$$ lines in the plane. These lines cut the plane in parts.

Of these parts exactly $$N$$ have a finite area.

Of these $$N$$ parts exactly $$K$$ are triangles.

Let $$x$$ be the maximum value of $$N$$ and let $$y$$ be the minimum value of $$K$$.

Find the value of $$x+y$$.

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