2004 AIME I Problem 6

An integer is called snakelike if its decimal representation a_1a_2a_3\cdots a_k satisfies a_i<a_{i+1} if i is odd and a_i>a_{i+1} if i is even. How many snakelike integers between 1000 and 9999 have four distinct digits?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.