Question 49
Let $p \ge 2$ be a prime number. Angelo and Vangelis play in turns the following game: At the board there are $p$ empty boxes, the one next to other, and in each move, the current player puts a digit in one of the boxes. Angelo plays first and the game ends after all boxes are filled and we get a $p$-digit number $M$, in which we allow zeros in the beginning. The goal of Angelo is to make the number $M$ divisible by $p$, and the goal of Vangelis is to prevent this. Prove that Angelo has a winning strategy.