Replace the addition problem captcha with a real analysis question. Even point set topology will do. The questions could have simple one-word answers, like "compact" or "manifold." That should keep out the riff raff.

may I suggest Let f be a mapping from a finite set D. Then f has a fixed point if and only if D is not a union of three_____ sets A, B
and C such that A \cap f(A)=B \cap f(B) = C \cap f(C)=\emptyset

Have found something even better there is an extension of something called the Caristi fixed point theorem called Kirk's problem that has a one word answer (yes, no) depending on circumstances. Howeve am sure this could be appropriately reformulated.

I quote: "A problem raised by Kirk [20-23, 29, 30] asked whether a Caristi type mapping T for a suitable
function \eta has a fixed point. In fact the original Kirk’s question was stated when \eta(t) = t^p for
some p > 1".