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?