Every handshake is a negotiation: how firm will it be? Some squeeze too soft, leaving their hand soft and limp. Others squeeze too hard, crushing their partner’s hand. And then there are those who squeeze just right — perfectly firm — and all is right with the world.

Is hand-shaking symmetric? If I think your shake was too firm, do you think mine was too limp? Can it be good for me, but not for you?

The handshake conjecture. Consider a single handshake. Let a and b be the firmness of the shake as perceived by the two shakers, A and B, respectively. Let perceived firmness take one of three values: -1 (limp), 0 (just right), or 1 (too firm). The conjecture states that a = -b.