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2007 iTest Problems/Problem 41

Revision as of 21:59, 7 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == The sequence of digits <math>123456789101112131415161718192021\ldots</math> is obtained by writing the positive integers in order. If the <math>10^{nth}</math> dig...")
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Problem

The sequence of digits $123456789101112131415161718192021\ldots$ is obtained by writing the positive integers in order. If the $10^{nth}$ digit in this sequence occurs in the part of the sequence in which the m-digit numbers are placed, define $f(n)$ to be $m$. For example, $f(2) = 2$ because the $100^{\text{th}}$ digit enters the sequence in the placement of the two-digit integer $55$. Find the value of $f(2007)$.

Solution

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