2022 OIM Problems/Problem 2
Problem
Let be the set of positive integers of the form , with . 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 . Borja wins if is divisible by a number belonging to , otherwise Ana wins. Find which player has a winning strategy and describe it.
Solution
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