## Monk Suicides

Here’s an intriguing puzzle I came across recently.  Have you ever been to a monk monastery?  It’s quite peaceful, and no one speaks to anyone else.  In a certain monastery near Tibet, all the monks have either brown or red eyes, and all the monks with red eyes are considered a curse and meant to commit suicide at midnight. For the time being let’s say there are 100 red-eyed monks.  But there is no way for a monk to see himself, and there is no communication between the monks, so there is no way for any of the red-eyed monks to know.

One day an unaware tourist comes to this monastery and says that at least one monk has red eyes.  Remember that these monks have reached a connection with God and therefore are perfectly rational.  What exactly happens?

If you don’t want to see the answer, don’t scroll below the picture.  Take some time to try it out for yourself.

To start to think about what happens, let’s first see what would happen if there was one red-eyed monk.  Well he would see no other red eyed monk, and so would fatally pierce himself with a blade that night.  Now what would happen if there was two monks?  None of them would do anything the first night, as they saw each other, but upon realizing that the other did not kill himself, they would both kill themselves on the second night.  This is because Monk A would see that Monk B would have killed himself if B saw only brown eyes, and there were no other red eyes other than A and B, so A would realize he also has red eyes.  What about with three monks?  For the first two days, none of the red-eyed  would be harmed because they would see two others.  But on the third day, after the doomed monks see that the other two did not take their lives, they will in the same way realize their own fates, and all three will leave this world (at least physically) on the third night.  I think you’re kind of getting the picture now. Given that there are n red-eyed monks, they will all kill themselves n nights from the unfortunate visit of the tourist.  So nothing happens at the monastery, and life goes on as usual (although there will be a visible concern among the monks), until the 100th night when all 100 of the red-eyed monks will die.  A darkly alluring puzzle this was…