Two minor comments. First, computer scientists don’t consider O(n^2) moves to sort “good,” since there are many O(n log_2(n)) algorithms out there. Order n^2 is adequate at best. Second, I think you might get somewhere with understanding what is happening with the n in the middle puzzle by considering the fact that each number has a specific number of moves it needs to make to get to the correct location. So when you do the explosions, you need to make sure the one is on the left edge all the time. There might be something said for small cases to explicitly build the full decision tree and see if 1/3 is in fact correct for n=3,5. That should be doable by pen and paper. Looks like a great open ended undergraduate research project! Steve On Oct 5, 2018, at 10:32 PM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: Yes, I should have written that. Jim On Friday, October 5, 2018, Michael Kleber <michael.kleber@gmail.com<mailto:michael.kleber@gmail.com>> wrote: For all of your comments about the number of explosions, are you actually looking at number of explosions *minus* number of un-explosions? Seems like you ought to be, but I don't think I've seen it mentioned yet. (Still reading though.) --Michael On Fri, Oct 5, 2018 at 4:44 PM James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: Usually I publish on the 17th, but this time I'm publishing on the 10th (in connection with Global Math Week). I'm not expecting many of you to spend your weekend hours perusing this, but even if only a couple of you do, I'm sure your comments will be helpful. https://urldefense.proofpoint.com/v2/url?u=http-3A__mathenchant.org_040-2Dse... Thanks, Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... -- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...