Two hundred and one perfect logicians with assorted eye colours are stuck in a deserted island. Of these, 100 have blue eyes, 100 have brown eyes and one has green eyes which however they don't know. These people can see everyone else (and hence know their eye colours) but they don't know their own eye colour (they don't even know the all colours present there)! Also, they cannot communicate with each other by any means. Every midnight a ship comes to the island and takes away only those people who know their own eye colour for sure at that point of time. The Guru (who happens to have green eyes) is allowed to speak one sentence to the islanders (at noon) after which no one speaks (communicates) and he says, "I see blue eyes!"
Now the question is: Who all leave the island and at what time?
Link to the Solution
9 comments:
some of them leave the island at some midnite ... :) .. and why would "perfect logicians" need our help anyways? .. :)
Clarification: The Guru is allowed to speak only once (in his whole lifetime) after which no one can communicate with each other by any means!
101 days
Every blue eyed guy is similar and every green eyed guy is similar. So all blue guys will leave on day X and all browns will leave on X + 1.
Take the case of 2 (1 blue, 1 brown). Blue eyed guy sees brown eyed guy and leaves on first night. Brown eyed guy (knowing that blue eyed guy left last night) can now be sure he has brown eyes and he leaves. So 2 days for 2 people.
Take case of 4 (2 blue, 2 brown) - everyone sees at least one blue eye. So no one leaves on first night. On second night, blue eyed guy knows that other blue eyed guy was not sure (which is why he didn't leave on first night), so I must also have blue eyes. So both blue eyed guys leave on second night and both brown eyed guys leave on 3rd night.
Extending this way, it will take 101 days for all of them to leave - on 100th day all blue eyed guys will leave, on 101st day all brown eyed guys will leave. Green eyed guy can leave any time he wants :)
@Manikandan: Nice solution but in your case of 2 people how does the brown eyed guy know that he has brown eyes on the 2nd day? They don't how many eye coloured people are there in that island!
thanks maanniik ... u saved me the trouble of writing the soln here ... :p
I don't get it. Can this be a solution.
Day I.
Guru says - I see blue eyes.
All 201 people claim their eyes are blue and 100 of them leave the island.
Day II
Guru says - I see brown eyes.
All 101 people claim their eyes are brown and 100 of them leave the island.
Guru stays. He becomes a martyr :D
@Vivek: No only those people leave the island who are certain about their eye colour. There is no probability involved here!
solution is as mani said .. except tht only ppl with blue eyes leave .. others cannot be sure about their eye colors .. is it?
@Yash: Absolutely correct!
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