A standard sixsided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the nth n appears.
Let P(n)=the probability the game terminates with the nth 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
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 20150730 09:11:20 