The 31st try resulted in them only solving the problem for odd m, but the even m case was still open. So of course this happened:

Filip also told me that he asked Claude to continue on the even case after the odd case had been resolved. “But there after a while it seemed to get stuck. In the end, it was not even able to write and run explore programs correctly anymore, very weird. So I stopped the search.”

Knuth did add a postscript on other friends maybe kinda vibing a possible solution for even m:

On March 3, Stappers wrote me as follows: “The story has a bit of a sequel. I put Claude Opus 4.6 to work on the m = even cases again for about 4 hours yesterday. It made some progress, but not a full solution. The final program . . . sets up a partial fiber construction similar to the odd case, then runs a search to fix it all up. . . . Claude spent the last part of the process mostly on making the search quicker instead of looking for an actual construction. . . . It was running many programs trying to find solutions using simulated annealing or backtrack. After I suggested to use the ORTools CP-SAT [part of Google’s open source toolkit, with the AddCircuit constraint] to find solutions, progress was better, since now solutions could be found within seconds.” This program is [4].

Then on March 4, another friend — Ho Boon Suan in Singapore — wrote as follows: “I have code generated by gpt-5.3-codex that generates a decomposition for even m ≥ 8. . . . I’ve tested it for all even m from 8 to 200 and bunch of random even values between 400 and 2000, and it looks good. Seems far more chaotic to prove correctness by hand here though; the pattern is way more complex.” That program is [5]. (Wow. The graph for m = 2000 has 8 billion vertices!)

I find it slightly funny how Stappers suggested to the AI to use specific external tools that are actually reliable (like ORTools). This also makes me question how much the of the AI's "insight" was a result of handholding and the rubber duck effect.

For context:

1. This is planned as a hard exercise for a textbook.
2. There are likely so many solutions that finding a general program that works (at least for enough values that you care to check) is like hitting the side of a barn with an arrow. Random bullshit go is an excellent strategy here.
3. The AIs did not provide proofs that their solutions worked. This is kind of a problem if you want to demonstrate that AI has understanding.