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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: Solution for n=2 and 3, and some observations Comment 14 of 14 |
(In reply to Solution for n=2 and 3, and some observations by puzzlesrfun)

57/81 + 17/81 + 6/81 = 80/81, not 1


The 17/81 should be 18/81. Something's missing from the set of terms you've added; there must be another term or one of the terms is wrong.

  Posted by Charlie on 2015-07-30 09:11:20
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