/prog/ challenge

A set of integers is sum-free when addition always gets you out of the set (i.e. x + y = z has no solutions -- in other words S + S and S are disjoint). Formally, let S be a subset of N. S is sum-free if for all a,b in S, a+b is not in S.

Now, let S be any set of nonzero integers. Find a subset of size > |S|/3.

You may use your favorite lisp language.

I've got a really nice solution for this one.

If S is sum free every subset of S is sum free. Let L be a subset of S and suppose x,y are in L. Because S is sum free and x,y are in S, we have x + y is not in S. Because L is a subset of S, x + y is not in L. Therefore, L is sum free.