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Math Help - Sum of digits

  1. #1
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    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?
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  2. #2
    Super Member
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    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.
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