TITLE: Sum of digits raised to a power
QUESTION [8 upvotes]: Let $S$ equal the sum of the digits of $2014^{2014}$.
Let $T$ equal the sum of the digits of $S$.
Let $U$ equal the sum of the digits of $T$.
What is $U$?

REPLY [6 votes]: I don't know what $U$ is, but I can give an upper bound for it. $$2014^{2014} < 3000^{3000} = 27000000000^{1000} = (2.7*10^{10})^{1000} < (10^{11})^{1000} = 10^{11000}$$
So $2014^{2014}$ is at most $11000$ digits long, which means $S$ is at most $99000$, which means $T$ is at most $9+8+9+9+9=44$, which means $U$ is at most $3+9=12$.