MathDB
NT game of writing digits

Source: Iberoamerican 2022, Day 1, P2

September 29, 2022
number theory

Problem Statement

Let S={13,133,⋯ }S=\{13, 133, \cdots\} be the set of the positive integers of the form 133⋯3133 \cdots 3. Consider a horizontal row of 20222022 cells. Ana and Borja play a game: they alternatively write a digit on the leftmost empty cell, starting with Ana. When the row is filled, the digits are read from left to right to obtain a 20222022-digit number NN. Borja wins if NN is divisible by a number in SS, otherwise Ana wins. Find which player has a winning strategy and describe it.
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