MathDB

2

Part of 2022 Iberoamerican

Problems(1)

NT game of writing digits

Source: Iberoamerican 2022, Day 1, P2

9/29/2022
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.
number theory