RMO 2025 Problem 1

(a)Let $n\geq3$ be an integer. Find a configuration of $n$ lines in the plane which has exactly

(i) $n-1$ distinct points of intersection. (ii) $n$ distinct points of intersection

(b) Give configuration of $n$ lines that have exactly $n+1$ distinct points of intersection for (i) $n=8$ and (ii) $n=9$ Proposed by Prof. C.R. Pranesachar