Timeline for A balls-and-colours problem
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8 at 9:17 | answer | added | user1467278 | timeline score: 0 | |
| Jan 24, 2011 at 19:32 | answer | added | Roah | timeline score: 2 | |
| Jan 2, 2011 at 18:22 | history | edited | domotorp |
edited tags
|
|
| Oct 14, 2010 at 6:22 | comment | added | Pratik Poddar | Of course, the mathematical solution is simple (though not elegant). I would like to see a more elegant solution. | |
| Oct 14, 2010 at 2:16 | comment | added | D. Savitt | I certainly didn't invent the problem. IIRC I heard about it at a colloquium tea in the MIT common room (not 100% sure from whom, but maybe Greg Warrington?), put it aside at the time, and brought it out as a challenge problem at Mathcamp later that summer. The rest of Rex's story is accurate, I think. | |
| Oct 13, 2010 at 18:49 | answer | added | David E Speyer | timeline score: 7 | |
| Oct 13, 2010 at 17:15 | vote | accept | Hedonist | ||
| Oct 13, 2010 at 15:31 | answer | added | Hugo van der Sanden | timeline score: 11 | |
| Oct 13, 2010 at 9:38 | comment | added | aorq | I first heard this problem at Mathcamp 2001. I believe the problem was invented there by Dave Savitt. I recall verifying it up to n=10 using linear relations among variables, one for each partition of n. Eventually, Dave and John Conway found a proof for all n. Their proof gave an explicit formula for the expected number of steps from any starting position, not just all distinct, and had a trivial inductive proof. IIRC, the formula involved harmonic numbers. While Ori Gurel-Gurevich's solution is very nice, I wonder if anyone can find the formula for all starting positions, which I have lost. | |
| Oct 13, 2010 at 6:44 | answer | added | Ori Gurel-Gurevich | timeline score: 30 | |
| Oct 12, 2010 at 23:54 | comment | added | David E Speyer | I think this question is borderline, but I would like to keep it open. It's borderline because you already know the answer, and that makes this more of a puzzle than a research question. On the other hand, I find "is there an elegant proof of this pretty combinatorial formula" to be a reasonable type of question. | |
| Oct 12, 2010 at 23:07 | answer | added | Ross Millikan | timeline score: 1 | |
| Oct 12, 2010 at 23:01 | answer | added | Aaron Meyerowitz | timeline score: 0 | |
| Oct 12, 2010 at 19:53 | history | asked | Hedonist | CC BY-SA 2.5 |