27015

If multiples of 3 are x, then there can't be three of x, x+1 or x+2. Also, you can't put one of each. Therefore, you must have one of these 2, which means it can always find a multiple of three, because you must have at least three numbers with the same connection to a multiple of 3 or x, x, x+1, x+1, x+2, or something like that