Problem

Source: Stars of Mathematics 2020 (senior level)

Tags: combinatorics, romania



Prove that, if every three consecutive vertices of a convex $n{}$-gon, $n\geqslant 4$, span a triangle of area at least 1, then the area of the $n{}$-gon is (strictly) greater than $(n\log_2 n)/4-1/2.$ Radu Bumbăcea & Călin Popescu