# Variant of blue eyes puzzle [closed]

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?

• This is now identical to the standard blue eyes problem. Commented Aug 4, 2021 at 13:57
• WIthout the guru from the blue eyes problem, there is nothing to kick start the process. If there were only one A, they would not be able to deduce they were an A without a guru pronouncement. Without that base case, no further deductions can be made. Commented Aug 4, 2021 at 14:33
• That's an extremely major change to the problem which might (I haven't thought it all through) completely invalidate the existing answer. I'm tempted to roll it back... Commented Aug 5, 2021 at 1:39
• @JaapScherphuis , I disagree with you . Imagine that there is only one A. His machine shows A's count to be 0. Yet, he notices that the game hasn't ended . This will tell him that he is A. Similar logic can be extended to the case of 2 As etc. Commented Dec 11, 2022 at 17:32
• @HemantAgarwal There were edits after my comment was made. Commented Dec 11, 2022 at 18:55