So I was reading about tilings and found really cool things like rep-tiles. Figures that can be assembled to get a homothetical figure. I was also reading about multiple solutions for the same tangram puzzle and I asked myself:
Could I take n identical tiles forming a figure A and take n+1 tiles identical to the ones I took before and form with them a homothetical figure to A?
I am specially interested in examples with small n. Can this problem be solved for n=4?
The triangle used in the pinwheel tiling can tile a homothetical figure using $4$ and $5$ copies.
More generally, a right-angled triangle with legs $1$ and $k$ is a rep-$k^2$ and rep-$(k^2+1)$ rep-tile.