Quote:
Originally Posted by vsuthichai
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.

Indeed, this is not allowed since the points have to be fixed in position; arbitrary but fixed. The game is to generate as many dichotomies as you can on a fixed set of (carefully chosen for this purpose) points.