Was it? It was an open problem to Knuth - who generally knows how to search literature. However there is enough literature to search that it wouldn't be a surprise at all to discover it was already solved but he just used slightly different terms and so didn't find it. Or maybe it was sovled because this is a specialization of something that looks unrelated and so he wouldn't have realized it when he read it. Or...
replyOverall I'm going with unsolved, because Knuth is a smart person who I'd expect to not miss the above. I'm also sure he falls for the above all the time even though the majority of the time he doesn't.
Agreed with all of that, but with the added point that Knuth has done a lot of work in this exact area in The Art of Computer Programming Volume 4. If he considers this conjecture open given his particular knowledge of the field, it likely is (although agreed, it's not guaranteed).
reply> If he considers this conjecture open given his particular knowledge of the field, it likely is (although agreed, it's not guaranteed).
replyIt is as good as guaranteed. If Knuth says it doesn't know how to solve the problem, and if anyone knows, then they will inform Knuth about it. Knuth not just a very knowledgeable person, but a celebrity also.
Also, if Claude had regurgitated a known solution, it would have come up with it in the first exploration round, not the 31st, as it actually did.
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