Problem 5. Can 100 lines be chosen in space so that they intersect at exactly 2022 points?
Answer. It is possible. Solution. Note that $43 \cdot 47=2021$. Therefore, if we draw 43 parallel lines in one direction and 47 parallel lines in another direction in some plane $\alpha$, we will already have 2021 intersection points. We will draw one more line so that it intersects the plane $\alpha$ at a point lying on one of the 90 already drawn lines, and the remaining 9 lines will be drawn parallel to the plane $\alpha$ at different distances from it, which will not add any new intersection points.

- For the answer "it is possible" without justification - 0 points.