Combinatorics in geometry

Geometry Level 3

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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