Red Eyed Monks

Well… a few days ago, I posted a little riddle about cursed monks on an island. Here’s the solution.

If you need to see the riddle again…

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide. Then one day a tourist visits the island monastery, and, not knowing that he’s not supposed to talk about eyes, he states the observation “At least one of you has red eyes.” Having acquired this new information, something dramatic happens among the monks. What happens?

Alright, let’s look at a few scenarios. First, let’s talk about how a monk would determine if his eyes were red. The easiest way to be assured of it, is if no one else on the island has red eyes. This being the case, if the tourist lied and there were 0 monks with red eyes, there would be mass suicide that evening. Why? Ever monk would assume that he/she had red eyes because no one else did, and there must be at least one, right? Right.

If one monk has red eyes, he’d commit suicide that night and it’d all be over.

It gets a little more tricky if more than one monk has red eyes, but lets logic through it. If two monks have red eyes, nothing will happen on the first night, but they’ll both commit suicide on the second night. Why?

Monk A and Monk B have red eyes. They each know that the other has red eyes. Everyone else on the island knows that two monks have red eyes. Since neither red-eyed monk will commit suicide on the first night (see above logic), then they must know that there are at least two monks with red eyes, therefore all monks who see only one other monk with red eyes will commit suicide.

With three red-eyed monks, they will not commit suicide on the first night because the cursed monks see two other monks with red eyes. On the second night, each cursed monk will hope that the other two commit suicide because, if they don’t, then they will each realize that they are the third monk. Accordingly, they’ll all commit suicide on the 3rd night.

The generalization is that the suicide will take place on the Nth night.

I think this riddle has one flaw, however: if more than one monk has red eyes, then they would not need the tourist to tell them anything. Therefore, given the facts presented in the riddle, one monk will commit suicide on the first night. Period. If more than one monk had red eyes, the suicide would’ve taken place before the toursit had a chance to tell them anything.

PS: Thanks goes to Batgrl for posting the comment that reminded me to post this answer.