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A positive integer $n$ is known as an interesting number if $n$ satisfies $$ \left\{\frac{n}{10^k}\right\} > \frac{n}{10^{10}} $$ for all $k=1, 2, \ldots, 9$, where $\{x\}=x - \lfloor x \rfloor$.

Find the number of interesting numbers.

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    What does the Curly brackets stands for? Something is missing perhaps?2011-07-07
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    @Amir Hossein What have you tried so far?2011-07-07
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    @Weaam, the curly brackets are for the *fractional part*, e.g., $\lbrace\pi\rbrace=.14159265\dots$.2011-07-07
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    Amir, can you do a simpler problem, say, $\lbrace n/10^k\rbrace\gt n/10^2$ for $k=1$?2011-07-07

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