Here is the puzzles link : http://www.wuriddles.com/
What happens if we change the tourist’s statement to each of the following?
“There are 10 Brown Eyed Monks”
“There are at lesat two Red Eyed Monks”
“There is an odd number of Red Eyed Monks”
“There is an even number of Red Eyed Monks”
“There is more than one Red Eyed Monk”
My Solution : If there are N people with red eyes among the group, then all the N people will commit suicide on the the N th night. Lets consider different scenarios.
If there is only one Red Eye monk, after the tourist announcing that there is at least one red eyed monk, this monk will look every one and finds that every one has blue eyes, which implies that he has the red eyes. So he will commit suicide that island on that night. So if there is only one Red eyed monk, it takes one day to decide.
Now lets consider, there are 2 red eyed monks. The first red eyed guy thinks in this way : I can see a guy with red eye and the remaining with blue eyes. So that red eyed guy must commit suicide today( by the first scenario). The second guy also thinks in the same way. So both will wait until tomorrow and no one commits suicide. Then the next day, both of them think in this way : If he is the only red eyed guy, he must have committed suicide by now, since he did not leave, there must be another red eyed guy, but i can see only one red eyed guy, that implies i am a red eyed guy. so the second night, both of them commit suicide.
Similarly, if there are 3 people, all the 3 people will commit suicide on the 3rd night. and the rest of the problems can be solved in the same way.
If you have any queries regarding the solution, please do post your comments.