Problem

Source: ELMO Shortlist 2024/C7

Tags: Elmo, combinatorics



Let $n\ge 2$ be a positive integer, and consider an $n\times n$ grid of $n^2$ equilateral triangles. Two triangles are adjacent if they share at least one vertex. Each triangle is colored red or blue, splitting the grid into regions. Find, with proof, the minimum number of triangles in the largest region. Rohan Bodke