The kinds of maze you often see as busywork have a single entrance and a single exit on the exterior wall, and have a single path between any two points in the maze. There's an algorithm for generating such mazes of arbitrary height when only the width is known in advance. I vaguely recall a story about Eller, the guy who came up with the algorithm, not thinking it was possible, but he heard that someone else had done it, so he worked it out---only to find that the other guy hadn't done it after all! Unfortunately, I can't find a source for this. On Fri, Apr 12, 2019 at 8:23 AM James Propp <jamespropp@gmail.com> wrote:
I've posted a draft of the essay I plan to post on the morning of the 17th (or maybe the night before) at
http://mathenchant.org/047-draft1.pdf
I don't expect to get comments from many of you, but all comments will be appreciated and acknowledged.
One thing that's missing from the essay is a good reference for readers who want to learn more about modern mazes. For that matter, do any of you know of any good references about how to create proofs that explicitly advocate the work-from-the-outside-in tactic? I've never read "How to Read and Do Proofs" or the many similar books that are out there, but if you think readers of my blog would like a particular book in this genre, I'd be glad to mention it.
Thanks,
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