## Nov 12, 2009

### Red-eyed monks and brown-eyed monks on an island?

There are 1000 monks living on an island, some with brown eyes and some with red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each monk can (and does) see the eye colors of all other monks, but has no way of discovering their own (there are no reflective surfaces).

All the monks are highly logical and devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).

Of the 1000 monks, it turns out that 100 of them have red eyes and 900 of them have brown eyes, although the monks are not initially aware of these statistics (each of them can of course only see 999 of the 1000 monks).

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, what effect, if anything does this have?

1. In case of one monk having red eye, when the tourist leaves he doesnt see any red eye so he knows that its him so he commits suicide that day. In case of two, when one of them wakes up the next day then he sees the other one alive and realizes that he also must be looking at one red eye. The other one also apply the same logic and commit suicide second day. With similar argument we can prove that all the 100 of them will commit suicide in the 100th night.

2. It's late here and I can't think clearly so I may be mistaken. Anyway, here's my two cents. From

"Of the 1000 monks, it turns out that 100 of them have red eyes and 900 of them have brown eyes"

and

"each monk can (and does) see the eye colors of all other monks"

it follows that every monk already knows that
1) at least 99 monks have red eyes and
2) every *other* monk knows that at least 98 monks have red eyes. Then
3) at least one monk has red eyes and
4) every monk knows 3)
is not new information at all, so nothing happens. Am missing something?

3. This comment has been removed by the author.

4. I agree with the anonymous!
Actually the trigger for suicides would be info on exact number of people with red eyes.
Presuming a situation like this, sounds more logical to me:
a) Initially the monks did not know how many among them were red eyed. They were living without suicides.
b)The tourist arrives and tells them that there are 100 red eyed.
c)Monks start taking a mental note of the red eyed monks they see.
d)Depending upon number of different monks they meet on a daily basis, say one red eyed monk realizes that he is red eyed because he saw all other monks and found only 99 red eyed. He waits for the midnight and suicides.
e) Assuming that all the monks which this first monk saw/met, also observed the color of his eyes, and that this presumption is true for all monks who observe the eye color, all the red-eyed monks will realize the true color of their eyes on the same day. Under such assumption, all monks suicide together, but it does not have to be hundredth day.
(To clarify the assumption- When monk, A observes the eye color of another monk, B; monk B simultaneously makes a note of the eye color of monk A.)
d) If the aforementioned assumption is not true, the monks will still suicide, but on different days. (Also another factor now would be - Does the news of suicide by one red-eyed monk reaches others instantly?)