Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 3"

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== Solution ==
 
== Solution ==
  
== See also ==
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== See Also ==
  
 
{{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}}
 
{{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}}
  
[[Category:Introductory Number Thoery Problems]]
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[[Category:Introductory Number Theory Problems]]

Latest revision as of 07:14, 19 July 2016

Problem

A $\emph hailstone$ number $n = d_1d_2 \cdots d_k$, where $d_i$ denotes the $i$th digit in the base-$10$ representation of $n$ for $i = 1,2, \ldots,k$, is a positive integer with distinct nonzero digits such that $d_m < d_{m-1}$ if $m$ is even and $d_m > d_{m-1}$ if $m$ is odd for $m = 1,2,\ldots,k$ (and $d_0 = 0$). Let $a$ be the number of four-digit hailstone numbers and $b$ be the number of three-digit hailstone numbers. Find $a+b$.

Solution

Solution

See Also

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by
Problem 2
Followed by
Problem 4
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