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If $d(n)$ is the sum of digits of n, find $d(d(d(n)))$ of $n=4444^{4444}$.

My attempt:


Now, $\max d(10000^{4444})<9\times 17776$

Again, $\max d(159984)\le 45$

Again $\max d(45)\le 12$

So, $\max d(d(d(n)))\le 12$.

Now, what am I supposed to do? Please help.


marked as duplicate by Henry, Mark Bennet, Eric Stucky, egreg, Claude Leibovici Apr 8 '14 at 8:15

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