April 8–April 14, 2008
Problem
For any integer k, define f(k) to be the square of the sum of the digits of k (writing k in base 10, as usual!). Next, define fm(k) = f(f(f(...f(k)))), where the function f is applied m times. For example, f2(35) = f(f(35)) = f(64) = 100.
The problem is to compute f2008(22008).
Solution
here.
List of solvers
Steve Wilmarth (undergrad); Dustin Moody (graduate); Konrad Schroder (staff); Stefan Sharkansky, Kate Smith, Mehran Asadi, Lloyd Sakazaki (outside).
Steve Wilmarth wins the prize!