Thoughts on the green-eyed logic puzzle, and the importance of meta-information

So I came across the Green-eyed logic puzzle from Ted-ed that goes: The problem There is an island with 100 prisoners, all of who have green eyes. All 100 prisoners are perfect logicians. They all want to escape the island. The condition of escaping the island is that one can deduce one’s own eye colour, and tell the guards the answer at midnight. If the answer is correct, the prisoner is set free.