4. (10 points) A square is divided into 2016 triangles, with the vertices of no triangle lying on the sides or inside another triangle. The sides of the square are sides of some triangles in the partition. How many points, which are vertices of the triangles, are located inside the square?
Answer: 1007

Solution. Let us have $k$ points inside the square. Then the sum of the angles of all triangles is $360 k+4 \cdot 90=180 \cdot 2016$ degrees.