Originally Posted by dsvick
OMK has a point - and not on top of his head either
In the set up you said that the prisoners were all told they were marked with either Green or Blue. So actually, as soon as there were at least 2 prisoners with each color, they should have been able to figure it out in X number of days, where X is the number of people marked with the least represented color.
Do the thought experiment - pretend you're the first prisoner to arrive, and you're given a green mark (although you don't know it's green). Subsequently one more green and two blue prisoners arrive. Every prisoner can now see at least one prisoner of each colour. So every prisoner knows that the prison contains prisoners of both colours. Can any of them conclude anything about their own colour from this? I think you will see that they cannot, especially if you try to consider the situation from the viewpoint of any one of the prisoners.