Note that any positive integer is either congruent to 0 mod 3 or 1 mod 3 or 2 mod 3. we have more than three integers here, so we know all congruences are accounted for. Further more, at least one congruence repeats. Try doing this by cases. (There may be an easier way, I'm not a Number Theorist)
Any questions? Do you have an idea of how to proceed?
EDIT: Ah, nevermind, I just realized this post makes no sense! Nothing is stopping us from choosing all the numbers of one congruence class