AT-OEMO-FED1 2018 Problem 3

Alice and Bob determine a number with $2018$ digits in the decimal system by choosing digits from left to right. Alice starts and then they each choose a digit in turn. They have to observe the rule that each digit must differ from the previously chosen digit modulo $3$ . Since Bob will make the last move, he bets that he can make sure that the final number is divisible by $3$ . Can Alice avoid that?

(Proposed by Richard Henner)