Sum of the digits of $N=5^{2012}$ The sum of the digits of $N=5^{2012}$ is computed.
The sum of the digits of the resulting sum is then computed.
The process of computing the sum is repeated until a single digit number is obtained.
What is this single digit number?

Hint : You can prove that if $d(n)$ denotes sum of digits of $n$, then $n$ is congruent to $d(n)$ mod 9. Also, $N<10^{2012}$ implies $d(N)<9*2012<20000$.
