Math Prize 2013 Problem 18
Source:
September 10, 2013
probabilityexpected value
Problem Statement
Ranu starts with one standard die on a table. At each step, she rolls all the dice on the table: if all of them show a 6 on top, then she places one more die on the table; otherwise, she does nothing more on this step. After 2013 such steps, let be the number of dice on the table. What is the expected value (average value) of ?