“So we could indeed condense the conditions into three points:
All boards of size 1xN, 2xN, 3xN, and 4xN, where N > 1, do not have a closed Knight’s Tour.
All boards of size NxN, where N is odd, do not have a closed Knight’s Tour.
All boards of size MxN, where both M and N are greater than 4, and the total number of squares is even, do have a closed Knight’s Tour.” – ChatGPT
Are these correct and if so are they all the conditions required for a closed knight tour to exist? Thank you.
In: 0
Wiki coulda helped you here, and it claims GPT is wrong. [Namely](https://en.wikipedia.org/wiki/Knight’s_tour#Existence), a 3×10 closed knight’s tour *is* possible (since it fails all three of the listed requirements for one to not exist), and your GPT answer claims otherwise. [Here’s a paper of the proof](https://web.archive.org/web/20190526154119/https://pdfs.semanticscholar.org/c3f5/e69e771771de1be50a8a8bf2561804026d69.pdf), which isn’t too too bad and doesn’t use anything too wildly advanced.
In general, m=3 and n=10, 12, 14, … have closed tours and are the exceptional examples. Otherwise, you need not-both-odd numbers > 4. So 5×6 works, 7×12 works, 9×9 does not work, 3×8 does not.
Latest Answers