Question 89
In the plane, $n$ lines are given, no two of which are parallel and no three of which pass through one point. By intersection points we mean all points in which some two of these lines intersect.
a. Prove that among the given lines there is one such that on each of its sides there are at least
$$
\left\lfloor\frac{(n-1)(n-2)}{10}\right\rfloor
$$
intersection points (points on that line are not counted).
b. For which values of $n$ can the estimate from part (a) not be improved?
a. Prove that among the given lines there is one such that on each of its sides there are at least
$$
\left\lfloor\frac{(n-1)(n-2)}{10}\right\rfloor
$$
intersection points (points on that line are not counted).
b. For which values of $n$ can the estimate from part (a) not be improved?