The total amount of money possessed by all 100 players is and this is constant throughout the games. Suppose the 63rd player has amount of money at the start. After 62 games, he will have money. The total amount of money of the other players is Thus, after the 63rd game, the 63rd player gives this amount of money in total to the other players, and he is left with in his pocket. The remaining 37 games are then played, after which the 63rd player has

Hence