1985 AIME Problem 10

How many of the first 1000 positive integers can be expressed in the form

\lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor,

where x is a real number, and \lfloor z \rfloor denotes the greatest integer less than or equal to z?

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.