So, as you can see, all the smaller triangles can combine to become bigger triangles, which is where the trick lies. If you count up every different triangle formed by the lines, you should get 24. (Don’t forget the big triangle!)
Some pedantic Quora users thought it through and realized there are even more triangles, if you really want to go there. There’s a triangle formed by the “A” in the signature in the right-hand corner, and if we’re counting the concept of triangles, the word “triangle” counts, too.
As math expert Martin Silvertant wrote on Quora, “A triangle is a mathematical idea rather than something real; physical triangles are by definition not geometrically perfect, but approximations of triangles. In other words, both the pictorial triangles and the words referring to triangles are referents to the concept of a triangle.” So yes, you could technically count the word “triangle.” (Silvertant also included a useful graphic explaining how to find all the pictorial triangles.)
Check out the whole Quora discussion for in-depth explainers from users about their methods of figuring it out.
[h/t Doctor ASKY]