2 player game with 2 bowls and 2019 balls
Source: 2019 Swedish Mathematical Competition p3
May 1, 2021
combinatoricsgamegame strategywinning strategy
Problem Statement
There are two bowls on a table, one white and one black. In the white bowl there balls.
Players and play a game where they make every other move ( begins).
One move consists is
to move one or your balls from one bowl to the other, or
to remove a ball from the white bowl,
with the condition that the resulting position (that is, the number of bullets in the two bowls) have not occurred before. The player who has no valid move to make loses.
Can any of the players be sure to win? If so, which one?