# Problem 7. (4 points)

On a plane, 13 points in general position are marked, some of which are connected by segments. In this case, the drawn segments do not form any triangles or quadrilaterals with vertices at the marked points.

Can more than 16 segments be drawn?

Points in general position - points, no three of which lie on the same line.
Answer: Yes

## Solution:

Since there should be no triangles or quadrilaterals, let's construct an example using pentagons:

![](https://cdn.mathpix.com/cropped/2024_05_06_a2fca548210b6e52e90eg-2.jpg?height=554&width=580&top_left_y=1979&top_left_x=264)

In the diagram, there are 17 segments. In fact, self-intersecting four-segment broken lines, which by definition are not quadrilaterals, could also have been used.