# 2004 AIME I Problems/Problem 6

## Problem

An integer is called snakelike if its decimal representation satisfies if is odd and if is even. How many snakelike integers between 1000 and 9999 have four distinct digits?

## Solution

We divide the problem into two cases: one in which zero is one of the digits and one in which it is not. In the latter case, suppose we pick digits such that . There are five arrangements of these digits that satisfy the condition of being snakelike: , , , , . Thus there are snakelike numbers which do not contain the digit zero.

In the second case we choose zero and three other digits such that . There are three arrangements of these digits that satisfy the condition of being snakelike: , , . Because we know that zero is a digit, there are snakelike numbers which contain the digit zero. Thus there are snakelike numbers.