Question 3
An equilateral triangle $\Delta$ has side length $L>0$. Inside it lie $n$ equilateral triangles of side length $1$ with pairwise non-overlapping interiors. Their sides are parallel to those of $\Delta$, but they have the opposite orientation. Prove $n\le\frac23L^2$.
Proposed by Alex Zhai. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p21499596. Source video https://youtu.be/9WNgDETHOlI?t=655.
Proposed by Alex Zhai. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p21499596. Source video https://youtu.be/9WNgDETHOlI?t=655.