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PostPosted: Thu, 23 Oct 2008 18:25:56 UTC 
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Say we have an increasing sequence of natural numbers, f. Given f(f(n))=3n, find f(100).

Edit: In case anyone wants to know, I mean strictly increasing.

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PostPosted: Fri, 24 Oct 2008 01:00:37 UTC 
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Spoiler:
181 :)

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PostPosted: Fri, 24 Oct 2008 01:24:22 UTC 
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A slightly trickier problem: Describe f by a piecewise function.

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PostPosted: Fri, 24 Oct 2008 20:10:46 UTC 
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Piecewise function:
Spoiler:
$ f(n) = \begin{Bmatrix} n + 3^k\ , &  3^k \le n \le 2\cdot 3^k \\ 3n - 3^{k+1}, &  2\cdot 3^k < n < 3^{k+1} \end

f(100) = 100 + 3^4=181 $ since $ 3^4 \le 100 \le 2\cdot 3^4

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