I'm having trouble understanding the problem. Picking an arbitrary triangle and N points, it seems simple to pick N points such that every point can be moved inside and outside the triangle effectively making h(x) equal to 1 or -1 at will. This obviously doesn't seem to be the correct line of thinking or else I would think the answer is just 2^N because all dichotomies are realized.

Do the chosen points within N need to consist of the three endpoints of the triangle? If that's the case, how does choice 'a' where N = 1 make up a triangle since it's only a singular point?

Any clarity is appreciated