Well, participation in the IMO 2009 Q6 polymath project has exceeded my expectations; it appears that the collaborative effort has scored some partial successes toward a solution in the first 24 hours of its existence, but is not quite there yet.
As the thread has become overly long, I am following established polymath practice and starting a new thread here, hopefully to try to impose more order onto the chaos. In order to assist this effort, some of the participants may wish to summarise some of the “state of play” so far. (I am unable to do this due to being biased by the knowledge of a solution.)
The comment numbering system has not worked as smoothly as I had hoped, but it is still better than nothing. I propose that comments in this thread start at 200, so as not to collide with the previous thread.
Of course, all the rules of the polymath exercise (as discussed in the previous thread) continue to apply. I am pleased to see that virtually everyone participating has adhered to the collaborative spirit of the exercise, for instance in keeping criticism constructive and technical rather than pejorative and personal.
As an experiment, I have enabled one level of comment threading; thus one can reply to a specific comment in the thread below. If one does so, I would request that you number the comment by subsection, for instance the first response to comment 234 would be numbered 234.1, the next one 234.2, and so forth. There is a tradeoff here; the threading adds more structure to the comments, but the flip side of this is that it makes it harder to read off at a glance all the comments made since the last time one checks the thread. Hopefully participants will be able to use their discretion when to reply and when not to. [Update, Jul 21: Threading should work properly now, I didn't set it properly before.]