Question 180
In a chess tournament there are $100$ players. On each day of the tournament, each player is designated to be 'white', 'black' or 'idle', and each 'white' player will play a game against every 'black' player. (You may assume that all games fixed for the day can be finished within that day.) At the end of the tournament, it was found that any two players have met exactly once. What is the minimum duration of days that the tournament lasts?