MathDB
k moves on right or lest in 2019 cells

Source: 2019 Chile National Olympiad level 2 p3

October 22, 2022
combinatoricsgamegame strategy

Problem Statement

Javiera and Claudio play on a board consisting of a row with 20192019 cells. Claudio starts by placing a token anywhere on the board. Next Javiera says a natural number kk, 1kn1 \le k \le n and Claudio must move the token to the right or to the left at your choice kk squares and so on. Javiera wins if she manages to remove the piece that Claudio moves from the board. Determine the smallest nn such that Javiera always wins after a finite number of moves.