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 Author Topic: 0.30 btc bounty: maths help (statistics)  (Read 13004 times)
lemonginger
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firstbits: 121vnq

 June 08, 2011, 08:45:49 PM

hours to work out? Come on people this is a permutations 101 question.

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ByteCoin
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 June 08, 2011, 10:39:32 PM

 0 _ 738035/120932352 1 _ 586435/10077696 2 _ 4301435/20155392 3 _ 33057475/90699264 4 _ 33616325/120932352 5 _ 1145495/15116544 6 _ 737353/181398528

I don't think it's a particularly easy problem.
An exact formula for the probability of no matches is

6^-12 * Sum_{k=1..6}(6-k)^6 * C(6,k) * Sum_{j=0..k} (-1)^(k-j) * C(k,j) * j^n

where C(a,b)=a!/(b!*(a-b)!)

but this is a simpler case than the other numbers of matches.

Possibly proper mathematicians have more powerful tools to bring to bear on such problems.

Explaining even this simple formula would take quite a lot of work but if you're willing to crack open a maths book then "Stirling numbers of the second kind" would be a good place to start.

ByteCoin
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 June 09, 2011, 05:44:41 AM

sorry i thought someone who is familiar with this kind of thing might be able to do it easily. i certainly didn't expect it to take 5 hours for the right person (although i admit it might take me 5 weeks to work it out).
kjj
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 November 02, 2012, 06:55:44 PM

Sorry for resurrecting this ancient thread, but I figure it is already in obsolete, so no one will care.

For some reason, I started thinking about this again.  I had forgotten the part about the Stirling numbers, but I had the "well, duh!" moment when I realized that 6^12 is only about 2 billion, and I might maybe be able to find some sort of computing device capable of iterating all of the combinations.

Code:
2176782336 Random Diff Stirling Diff
0   13284630 0.6103% 0.61% -0.0016% 0.6103% 0.0000%
1  126669960 5.8191% 5.82% -0.0028% 5.8191% 0.0000%
2  464554980 21.3414% 21.33% 0.0081% 21.3414% 0.0000%
3  793379400 36.4473% 36.43% 0.0213% 36.4473% 0.0000%
4  605093850 27.7976% 27.80% 0.0010% 27.7976% 0.0000%
5  164951280 7.5778% 7.60% -0.0232% 7.5778% 0.0000%
6    8848236 0.4065% 0.41% -0.0028% 0.4065% 0.0000%

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