## Problem 8'.3. (Problem for the UBM award)

Is it possible to find 100 straight lines in the plane such that there
are exactly 1998 intersecting points?


Solution: Consider 99 lines such that 73 of them are parallel and the remaining 26 lines pass through a single point and intersect all 73 parallel lines. Then the total number of intersecting points is $73 \cdot 26+1=1899$. Choose the last line in such a way that it intersects all lines and does not pass through any of the points. Now there are $1899+99=1998$ intersecting points.
