MathDB

On a table, there are many coins and a container with two coins. Vale and Diego play the following game, where Vale starts and then Diego plays, alternating turns. If at the beginning of a turn the container contains

n

coins, the player can add a number

d

of coins, where

d

divides exactly into

n

and

d < n

. The first player to complete at least 2024 coins in the container wins. Prove that there exists a strategy for Vale to win, no matter the decisions made by Diego.

Problem Statement