[math-fun] Conway's Problem C

I finally figured out what I am now sure is the answer. My original thought was that because a) If all pairs are unlinked, there cannot be any further linking, since such "Brunnian" links are impossible with round circles; b) If each pair is linked, there are only two topological possibilities for a triple link and they are mirror images; therefore the only answer seemed to be 0 key-rings. But not very likely as the intended answer. Now I realize what Conway meant. Pretty darn tricky! But fair. —Dan