MathDB

n

is a positive integer. An equilateral triangle of side length

3n

is split into

9n^2

unit equilateral triangles, each colored one of red, yellow, blue, such that each color appears

3n^2

times. We call a trapezoid formed by three unit equilateral triangles as a "standard trapezoid". If a "standard trapezoid" contains all three colors, we call it a "colorful trapezoid". Find the maximum possible number of "colorful trapezoids".

Problem Statement