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.

(In reply to Solution for n=2 and 3, and some observations by puzzlesrfun)

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

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