Each of the 100 people there must shake 99 hands. But if I shake your hand, this is one handshake, not two, so divide 9,900 by two. The answer is 4,950.

One might have thought that someone trained in mathematics or science would answer this easily by applying rigorous logic, while a student of the humanities might flounder. (Incidentally, C. P. Snow's Rede Lecture which started the Two Cultures controversy was given in Cambridge just half a century ago.) But it's not quite as simple as that.

A teacher of mathematics of my acquaintance (no names, she knows who she is) talked about factorials for a bit, then decided that it involved triangular numbers and gave up. Another acquaintance, equally intelligent, who had studied Latin and Greek, went off at a tangent and got it wrong.

My guess is that anyone with a bit of gumption can solve it easily unless he or she is side-tracked by a bit of irrelevant knowledge or excessive cleverness.

Now you can tell the person of integrity either to burn the envelope or to open it and admire your gumption.