2022 OIM Problems/Problem 2

Problem

Let $S = {13, 133, 1333, \cdots }$ be the set of positive integers of the form $1\overset{n\text{-digits}}{\overbrace{3\cdots 3}}$ , with $n \ge 1$ . Consider a horizontal row of 2022 empty cells. Ana and Borja play the following game: in turn, each player writes a digit from 0 to 9 on the leftmost empty cell. Starting with Ana, the players take turns until all cells are filled. When the game ends, the row is read from left to right to create a 2022-digit number $N$ . Borja wins if $N$ is divisible by a number belonging to $S$ , otherwise Ana wins. Find which player has a winning strategy and describe it.

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2022 OIM Problems/Problem 2

Problem

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