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Find the number of interesting numbers

Source: China TST 2011 - Quiz 1 - D1 - P3

May 19, 2011
number theory proposednumber theorycombinatorics

Problem Statement

A positive integer nn is known as an interesting number if nn satisfies  {n10k}>n1010{\ \{\frac{n}{10^k}} \} > \frac{n}{10^{10}} for all k=1,2,…9k=1,2,\ldots 9. Find the number of interesting numbers.
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