16
Dec
09

Solutions to WU’s puzzles and riddles : Brown eyes and Red eyes (medium)


BROWN EYES AND RED EYES

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers … :)

Here is the puzzles link : http://www.wuriddles.com/

Question: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?Hint: First consider the case where there are only a few monks on the island, some with brown and some with red. Work through the logic and find out what happens over time. Then generalize for the case of M monks on the island, N of which have red eyes.

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.

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10 Responses to “Solutions to WU’s puzzles and riddles : Brown eyes and Red eyes (medium)”


  1. December 17, 2009 at 5:59 pm

    Explain the case with 3 red-eyed monks in detail please…. And also how did you generalize?

    • 2 karavi
      December 18, 2009 at 4:01 am

      Hi Astrix …..
      I guess you got the logic up to 2 red eyes.
      Now lets say there are 3 persons with red eyes, then the first red eyed guy will think in this way : ” According to the previous 2 red eyed logic, these 2 red eyed people must leave after 2 nights. So i will wait for 2 nights and see”. In the same way other 2 red eyed guys also think. So on the third day, all of them will see each other and then think that since these 2 did not commit suicide, there must be one more guy with the red eye . but i can see only 2 red eyes, which implies i am the third red eye guy. So this is the logic for 3 red eyed guys. They will commit suicide after 3 nights.

      Similarly for 4 red eyed guys, it will 4 days as the 4th red eyed guy will wait for 3 days for the 3 red eyed guys to commit suicide. if they dont commit suicide for t3 days, then all the 4 people will commit suicide on the 4th day.

      By using Mathematical induction, we can generalize this to N red eyed people ….. :)

      I hope thats clear, if you still have doubt, call me ra bakka …..

      • 3 Vimal
        October 18, 2013 at 8:31 am

        Just came by this solution while googling. I don’t think this is a solution, for any of the case. Just take the case of two red eyed guys. There is chance for a brown eyed person to think that he is red eyed, You missed that!.

      • 4 Mav
        November 11, 2013 at 5:35 am

        Vimal: no there isn’t

        the two red-eyed monks would commit suicide before any brown-eyed monks have a chance to. a brown-eyed monk wouldn’t commit suicide until the third day, but by that point the red-eyed monks are already dead

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    July 4, 2013 at 2:31 am

    since there is no way for the monks to see which of them had the red eyes they would all commit suicide

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