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 computer aided solution by Charlie)

As Brother Ady would say, "Computer wins".

Posted by Steve Herman on 2015-07-01 18:48:00