There are a total of 200 players assigned to either A or B at a certain venue. There are actually 100 of each, but the players don't know that. They don't know which one they are. Of course, there is no way to exchange information with others.
If you are logically certain that you are A, you leave immediately; B stays. Each player has a machine that displays the number of other A and B players remaining excluding the machine-holder in the venue every five minutes. The machine keeps track of rounds it shows the rest of the A and B players and it starts as round zero.
The game will end when there are no A's.
Assume that all the players have sufficient logical thinking ability. How many rounds will it be, in the shortest case, before there are no more A's in the venue, i.e., all the machines display that there are no A's?