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One 1 to Six 6's (Posted on 2015-07-01) Difficulty: 4 of 5
A standard six-sided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the n-th n appears.

Let P(n)=the probability the game terminates with the n-th n.

Find the distribution of n.

Feel free to generalize for m sides.

Warning: I have not managed this past m=4.

No Solution Yet Submitted by Jer    
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re(2): more results (11 and 12) | Comment 12 of 14 |
(In reply to re: more results (11 and 12) by Daniel)

12-sided die:

I didn't really expect those ratios to be quite √10, but I did expect them to have a more regular behavior.  That down and up is a bit of a shock.

  Posted by Jer on 2015-07-05 16:07:34
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