Timeline for Approximate search space on a 5x5x5 cube with 3 different possible classes?
Current License: CC BY-SA 2.5
11 events
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| Apr 2, 2011 at 21:30 | history | edited | prelic | CC BY-SA 2.5 |
added 198 characters in body
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| Apr 1, 2011 at 16:31 | vote | accept | prelic | ||
| Apr 1, 2011 at 8:52 | answer | added | Douglas Zare | timeline score: 4 | |
| Apr 1, 2011 at 8:36 | answer | added | Gerhard Paseman | timeline score: 0 | |
| Apr 1, 2011 at 7:35 | history | edited | prelic | CC BY-SA 2.5 |
added 143 characters in body
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| Apr 1, 2011 at 7:32 | comment | added | prelic | Excellent insight, I didn't even think about that because of the way I was doing the simulation, but that's certainly another constraint | |
| Apr 1, 2011 at 6:54 | comment | added | Douglas Zare | Of course, requiring the difference in counts to be $0$ or $1$ only reduces the number by about a factor of $11$. | |
| Apr 1, 2011 at 6:47 | comment | added | Douglas Zare | Do you really need to consider boards with $10$ noughts and $5$ crosses? | |
| Apr 1, 2011 at 5:50 | comment | added | prelic | Thanks sir, that was the next step if I didn't get an approximation on here. If you change your comment to an answer I'll give it the check. | |
| Apr 1, 2011 at 5:30 | comment | added | Logan M | If all you need is an estimate, I'd run a Monte Carlo code. Something like: 1) Randomly generate a position 2) Check if it's a valid position or not 3) Check under what rotations, reflections the position is invariant. 4) Repeat Once you have a lot of trials (a computer can easily do a few billion), sum the reciprocals of the numbers from step 3 of those positions which were valid. Then estimate from this the probability that a randomly chosen configuration fits your criteria, and multiply by the number of positions (3^125), for a decent estimate. | |
| Apr 1, 2011 at 5:09 | history | asked | prelic | CC BY-SA 2.5 |