Please comment your solutions, questions and remarks..
There are infinitely many prisoners in a prison. The prisoners are taken to the yard and everyone is given a hat which is either black or white. No one knows the colour of his or her own hat, but sees the other’s hats. Then everyone have to guess his or her own hat’s colour. Those who guess correctly are given freedom. The prisoners knew about this event in advance and have had some time to agree on a strategy. How can they agree such that
(a) infinitely many of them get freedom? Level 1/5
(b) only finitely many of them stay in the prison? 4/5
The prison looked like this btw: