Hint to Riddle of the Week

Hint to Riddle of the Week: The Blue-Eyed Islanders

Difficulty level: Very Hard

Michael Stillwell
 
By Jay Bennett

It is nearly impossible to solve this problem without simplifying it first. So ask yourself this question: What if only one person on the island had blue eyes, and the other 199 had brown eyes? Well, seeing everyone else with brown eyes (and the guru with green), the fellow with blue eyes would realize he must be the person the guru was referring to when she said, "I see a person with blue eyes." And so he would leave that very first night when the ship comes to the island.

Okay, now imagine that there are only two people with blue eyes and 198 with brown eyes. What would happen? Each blue-eyed person would look around and see 198 brown-eyed people, and the single other person with blue eyes. They would think to themselves: "If that person is the only one with blue eyes, then they will leave tonight on the ship." But the next morning, the other blue-eyed person is still on the island. So now each blue-eyed person thinks: "That person with blue eyes didn't leave. Therefore there must be another person with blue eyes, and because I do not see anyone else with blue eyes, it must be me."


Michael Stillwell

The two blue-eyed islanders in this scenario realize this at the same time—on the morning of the second day when they see the other hasn't left. (They are perfect logicians, after all.) They both leave on the second night.

Now, what would happen if three of these logicians had blue eyes, and the other 197 had brown?