2019 Fall Team #10
Source:
April 17, 2022
combinatorics
Problem Statement
players are playing a game. Each player has tokens. Every turn, two players with at least one token are randomly selected. The player with less tokens gives one token to the player with more tokens. If both players have the same number of tokens, a coin flip decides which player receives a token and which player gives a token. The game ends when one player has all the tokens. If , suppose the maximum number of turns the game could take to end can be written as for integers . Find
.