Disclaimer: The solutions we've shared are just one exciting approach, and there are surely many other wonderful methods out there. We’d love to hear your alternative solutions in the community thread below, so let's keep the creativity flowing!

Definition: Call flipping the sides of three coins that are touching each other a move. Alternating a triangle of size $n$ means flipping the sides of all the coins of that triangle by performing a series of moves.

A. Perform moves on the three corner triangles of size $1$ one by one and then perform a move on the center triangle of size $1$.

B. We prove this by induction. Base case $n=3$ is already shown. Now suppose we can alternate a triangle of size $n=3k$. We will show that we can also alternate the triangle of size $n=3(k+1)$. In this triangle, first alternate the top $3k$ part. Then, the remaining bottom three rows can be divided into parts like below:

There will be a triangle of size $1$ or $3$ at the end depending on whether $n$ is even or odd. Notice that all these parts can be alternated easily and we are done.