Difference between revisions of "2004 AIME I Problems/Problem 15"

 
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== Solution ==
 
== Solution ==
 +
{{solution}}
  
 
== See also ==
 
== See also ==
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* [[2004 AIME I Problems/Problem 14| Previous problem]]
 +
 
* [[2004 AIME I Problems]]
 
* [[2004 AIME I Problems]]

Revision as of 01:46, 6 November 2006

Problem

For all positive integers $x,$ let

$f(x)=\begin{cases}1 & \rm{if \ x=1}\\ \frac x{10} & \rm{ if \ x \ is \ divisible \ by \ 10}\\ x+1 & \rm{otherwise}\end{cases}$


and define a sequence as follows: $x_1 = x$ and $x_{n+1} = f(x_n)$ for all positive integers $n.$ Let $d(x)$ be the smallest $n$ such that $x_n = 1.$ (For example, $d(100)=3$ and $d(87)=7.$) Let $m$ be the number of positive integers $x$ such that $d(x)=20.$ Find the sum of the distinct prime factors of $m.$

Solution

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See also