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#Post#: 108--------------------------------------------------
Blue Eyed People Island
By: kranthipls Date: November 18, 2012, 11:23 pm
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On an island, there are k people who have blue eyes, and the
rest of the people have green eyes. There is at least one
blue-eyed person on the island (k ≥ 1). There are no
mirrors or reflective surfaces on the island. So a person does
not know the colour of his own eyes. He can see the colour of
other's eyes. They cannot communicate among-st each other about
other's eyes' colour (assume that they are dumb for
convenience). If a person knows that he has blue eyes he can
leave the island that evening. There will be plane everyday
evening at the island. Only the blue eyed people in the island
are allowed to leave the island using the plane.
The problem: assuming all persons on the island are completely
logical and that this too is common knowledge, what is the
eventual outcome?
i.e If there are k blue eyed people on the island how many days
does it take all the blue eyed people to leave the island?
#Post#: 138--------------------------------------------------
Re: Blue Eyed People Island
By: adi Date: November 19, 2012, 3:05 am
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k = 1
outsider says there is a blue -eyed person
green guys find a single blue eyed person : they do not go
blue guy finds everyone else green leaves : 1day
k =2
outsider says....
green guys find two blue guys
blue guy 1 finds all green guys and a blue guy
blue guy 2 same
blue guy 1 finds blue guy 2 not leaving on day one both leave on
day 2
try for k > 2 :o
#Post#: 140--------------------------------------------------
Re: Blue Eyed People Island
By: kranthipls Date: November 19, 2012, 3:20 am
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Hey do not get confused. Outsider just comes and says that there
is atleast one blue eyed person amongst you. He doen't give the
total number of blue eyed people. He doesn't come everyday. He
just comes one day and goes off
#Post#: 146--------------------------------------------------
Re: Blue Eyed People Island
By: dinesh Date: November 19, 2012, 9:45 am
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all try to enter the plane. If they are not allowed they come
back. All blue eyed people can get in. In one day, all blue eyed
people can leave!!!
#Post#: 148--------------------------------------------------
Re: Blue Eyed People Island
By: kranthipls Date: November 19, 2012, 10:06 pm
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They go to the plane only if they are sure that they have blue
eyes. They are highly intellectual people.
They does what they think and they think what they do........
#Post#: 151--------------------------------------------------
Re: Blue Eyed People Island
By: kpr29 Date: November 19, 2012, 10:10 pm
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@Kranthi: The quote in matrix is............ "Dont think who u
are.............. Know who u are........."
#Post#: 153--------------------------------------------------
Re: Blue Eyed People Island
By: kranthipls Date: November 19, 2012, 10:21 pm
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@kp You are wrong. My version is correct, you can
check..........I just now checked it on internet
#Post#: 157--------------------------------------------------
Re: Blue Eyed People Island
By: kpr29 Date: November 19, 2012, 10:33 pm
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@Kranthi: S...... Stand corrected..........
#Post#: 163--------------------------------------------------
Re: Blue Eyed People Island
By: kranthipls Date: November 19, 2012, 10:52 pm
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Hint: Please use induction
#Post#: 178--------------------------------------------------
Re: Blue Eyed People Island
By: kranthipls Date: November 20, 2012, 10:03 am
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Answer:
Let us go by induction.
K=1 If there is only one blue eyed man then he sees all the
remaining people's eyes and since all have green eyes he decides
he is the one and goes on the first day.
K=2 If there are humans with blue eyes one sees the other and
both thinks that the other goes on the first day.
On the next if they again see each other and since none
of them left on first day they conclude that they have blue eyes
and leave on second day. So it takes 2 days.
The same logic can be applied for any number of days and if
there are k blue eyed people they all leave the island on the k
th day.
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