\(L=\)

An equilaterla triangle \(T\) of side length \(L > 0\) is given. Suppose htat \(n\) equilateral triangles with side length 1 and with non-overlapping interiors are drawn inside \(T\), such that each unit equilateral triangle has sides parallel to \(T\), but with opposite orientation. Prove that \( n \leq (2/3) L^2 \).

© 2023 __Peter E. Francis__