The FQ thread created earlier today (Geometry buffs: Pls explain this “How many triangles” puzzle) reminded me of a mathematics competition I participated in years ago. One question was similar, and I’ll pose it here.
(First, my sketches aren’t great. Please assume the triangles I sketched are all equilateral.)
The question goes like this —
If this is a triangle of side length = 1,
where you can see 1 triangle,
and if this is a triangle of side length = 2,
where you can see 5 triangles,
then how many triangles can you see for a triangle whose side length = 10?