But I think Conway's problems B and C were really masterpieces.
-- more precisely, I think the phrase I was looking for is "masterpieces of sadism." In problem C, it was somewhat mysterious what Conway had meant by "distinguishable even though I've never been able to tell left from right." All his rings must have EXACTLY the same diameter and made of exactly the same metal of same thickness etc otherwise I could distinguish them even without telling left from right. But then it is impossible to pass two rings thru each other's hole. And then, if I have a ring R, and I have (say) 9 others all linked with R, they will have a unique ordering clockwise round R since cannot pass thru each other. So this whole global-ordering issue really messes things up about distinguishability and about my whole argument about "two-graphs." We might indeed then argue that all the two-graphs are eliminated except perhaps for a very small finite set, whereupon the answer to Conway's question is "the empty set" or perhaps {5}, {9}, or {5,9} but I can't believe it could be more. But that would be too easy to get right by randomly guessing the answer, so Conway could not have meant that. So really, you sort of had to guess what Conway meant with his sadistically-chosen kind of vague wording, as part of the problem, e.g. what distinguishing methods he was going to allow. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)