Follow-up: Royal Order of the Garter

Last week, we posed a question about the Royal Order of the Garter. However, my intuition about the problem was, alas, incorrect.

(If things had worked out the way I thought they would, it would have turned out that twenty-three knights could have cycled around longer than twenty-five, and that King Edward III got the rule exactly right for twenty-five knights)

But I think this is a good illustration of the way mathematicians actually work; we try to get some intuition, make a guess, and then prove the guess is correct. Sometimes it isn’t, and we have to try again. We’re often drawn to elegant solutions, and quite often these turn out to be right. But sometimes, they just aren’t.

Usually, this is done in private, not on a podcast.

Because of time contraints, we deleted a discussion of all of this from this week’s segment, but here it is.