2022 OIM Problems/Problem 2

Revision as of 02:35, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>S = {13, 133, 1333, \cdots }</math> be the set of positive integers of the form <math>1\overset{n\text{-digits}}{\overbrace{3\cdots 3}}</math>, with <...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://sites.google.com/uan.edu.co/oim-2022/inicio