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?

Let $f(n)$ denote the sum of sum of ... sum of digits of $5^n$, then:
$f(n)=\cases
 {
  1 & $n\equiv0\pmod6$\\
  5 & $n\equiv1\pmod6$\\
  7 & $n\equiv2\pmod6$\\
  8 & $n\equiv3\pmod6$\\
  4 & $n\equiv4\pmod6$\\
  2 & $n\equiv5\pmod6$\\
 }
$
Therefore: $2012\equiv2\pmod6 \implies f(2012)=7$.
