Monks Puzzle Solution

Examine situation if there is only one monk. That monk goes out and sees there is no other monk with brown eyes. He must assume that he has brown eyes. He then goes back to his quarters and kills himself.
Now if there were 2 monks with brown eyes- on the first day the two would each see the other's brown eyes and that all the other monks are blue. When they return the next day they would see that the other guy is still alive, so they must assume that they have brown eyes under the assumption that the other would have killed himself if he had not seen any other monks with brown eyes.
For three monks it would take 3 days for the brown eyed monks to be sure that they have brown eyes. This follows since the monks are smart and would have been able to come up with the case for two brown eyes, and upon not seeing the two other guys with brown eyes kill themselves, the third monk would know on day three that he was therefore brown. The third monk in this case would be the one guy that looked out and only saw two other brown eyed monks.
It then follows inductively that for an n number of brown eyed monks, the brown eyed monks will kill themselves on day n after the decree is made.

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