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IOQM 2023-24 P-18

Source:

September 3, 2023

Problem Statement

Let P\mathcal{P} be a convex polygon with 5050 vertices. A set F\mathcal{F} of diagonals of P\mathcal{P} is said to be minimallyfriendlyminimally friendly if any diagonal d∈Fd \in \mathcal{F} intersects at most one other diagonal in F\mathcal{F} at a point interior to P.\mathcal{P}. Find the largest possible number of elements in a minimally friendly\text{minimally friendly} set F\mathcal{F}.
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