# Sum of digits

• November 4th 2012, 04:25 PM
makramer
Sum of digits
$S(n)$ is the number of digits of $n$. Is it possible to calculate:

$S(S(S(S(2012!^{2012!}))))$

Can You help me with this exercise?
• November 4th 2012, 06:41 PM
richard1234
Re: Sum of digits
...Eek. That is a large number.

You could try "guessing" at values for the answer, then using that guess to put a lower bound and upper bound. For example, if $S(S(k)) = 2$, then $10^9 \le k \le 10^{99} - 1$.

Don't know if that method'll work but it's the only feasible method I see...problem is you'll have to determine between which two bounds $2012!^{2012!}$ lies between. Have fun with that.