Mock AIME 5 2005-2006 Problems/Problem 3

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 $a+b$ .

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by Problem 2	Followed by Problem 4
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Mock AIME 5 2005-2006 Problems/Problem 3

Contents

Problem

Solution

Solution

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