A warden lines up these prisoners. He announces, "I see a white hat." He then leaves the room. Every few minutes he comes back in and asks if anybody knows their hat color. Anyone who figured it out before the warden came back must announce "I do", after which he is freed. Everyone else must remain silent until the next visit. After a prisoner is freed, everyone else will know who was freed.
- each prisoner knows that there are 8 prisoners (including themselves), each with a hat, lined up in this orientation
- each prisoner can see the hat color of all the prisoners in front of them (not their own or those behind them)
- the prisoners cannot move or communicate at all, beyond announcing to the warden that they know their hat color
- each prisoner is a logician
Who (if any) figures out the color of their hat, and when?