Well... there are other such scenarios. Spend 6 hours brainstorming on an idea. Only mention FAILED ideas aloud amongst your fellow Turn-clones. Do so in a manner that requires "keying" to what specifically you're thinking about at the time. (Such as minutes-into-the-hour). After 6 iterations, acquire profit.
This has the added advantage that it follows the "DO NOT MESS WITH TIME" restriction of following by rote.
I'm not sure I understand what you mean by "keying." Could you elaborate, and explain how you end up with a scenario that is more stable from "Time's perspective" than, say, clone #5 just summarizing all the ideas at the beginning of the hour? The scenarios I can come up with seem to involve information magically appearing (which the universe doesn't seem to like, as in Harry's integer factorization algorithm), or fail to provide a benefit over just thinking on one's own for six hours.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: