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Logic Puzzles from multiple points of view 2/5

July 1, 2009 am31 7:17 am

Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.

None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.

Green-eyed Guru

On a wonderful, magical island live 201 enchanted islanders. One hundred have blue eyes, one hundred have brown eyes, and one, the Guru, has green eyes.

None of the islanders knows their own eye color. There are no mirrors. Water does not reflect. Good thing, too, since upon learning his or her eye color, an islander would have to, at the next midnight, swim off the island (through shark-infested waters, if you don’t mind scaring your students)

And none of the islanders can speak, except the Guru. But the Guru sleeps and sleeps and sleeps, wakes up once every hundred years, says something, and goes back to sleep.

The day for the Guru’s waking comes, and all the islanders gather around her, expectantly. She opens her green eyes, stretches, and says

  • I see someone with blue eyes

and goes back to sleep.

Who leaves the island, and when. Explain your reasoning.

Place questions/clarifications below. To submit proposed solutions, click here.

11 Comments leave one →
  1. Kelly permalink
    July 2, 2009 pm31 11:27 pm 11:27 pm

    The tallest one, that night? (The guru stretched….)

  2. Kelly permalink
    July 2, 2009 pm31 11:29 pm 11:29 pm

    Or maybe everyone with blue eyes? I mean, they all start looking at each other, pointing, miming “Is it me?” and nodding when the answer is yes… and 100 go jump in the water that night.

    • July 3, 2009 pm31 4:11 pm 4:11 pm

      No miming. This island is near-paradise.

  3. Colleen permalink
    July 10, 2009 pm31 4:31 pm 4:31 pm

    No one leaves, as no one knows their own eye color.

    • July 11, 2009 pm31 1:15 pm 1:15 pm

      Actually, when the guru speaks, that little piece of information sets all their brains in motion. Think about it this way:

      If there were just the guru, 1 blue eyed person, and 1 brown eyed person, and the guru says “I see someone with blue eyes.” what will they figure out? When will they figure it?

      Then try the problem again, but add 2 more people. See what happens.

      In the end, it’s pretty amazing.

  4. July 11, 2009 pm31 5:24 pm 5:24 pm

    I think more information is needed in this puzzle.

    The natives cannot know everything that you have given in the intro, because if they knew exactly how many people have which color of eyes, they would all be able to figure out their own eye color, and no one would be left to hear the Guru.

    On the other hand, they *do* need to know that the only possible eye colors are blue and brown, or else they would all be safe until the Guru specified, “I see 100 blue-eyed people.”

    • July 11, 2009 pm31 5:28 pm 5:28 pm

      In the simpler puzzle with 1 brown and 1 blue (and the guru), what happens, and when?

      The second step is the biggest step. In the next simplest puzzle, with 2 brown, 2 blue (and the guru), what does each person see? What do they expect to happen? What actually happens?

      This is truly a remarkable puzzle. I would certainly play a bunch more before peeking at the solution.

  5. Marius Ilinca permalink
    July 15, 2009 am31 11:56 am 11:56 am

    The puzzle works for a few singular cases only.If there were only one or two blue eyed or brown eyed persons, after getting the information that “there are blue eyed persons” then they(the blue eyed ones) will leave the second day if they were 2 or the first day if that person was the only one with blue eyes.
    Now comes the problem:
    If there were 3 ore more blue eyed or brown eyed persons they would have already left the n-th day after they first saw each other(where n is the number of blue/brown eyed persons in the village)
    This is because “every blue eyed person already knew that every other blue eyed person knew that there are(at least 1 in the case of 3 persons) blue eyed persons amongst them”.
    This is the information given by the guru,”the trigger” so to speak, which in this case was already in place the first day that everyone saw each other.
    The explanation is simple for one or 2 persons in cause(blue eyed let’s say).And when you add another (blue eyed)person you just place yourself in her/his shoes and think about every other (blue eyed)person as the group that has to leave the day specified(the second in the case of 2 persons).When you see that they didn’t leave you conclude that there is one more.Since you see no other blue eyed persons you conclude that it can only be you and have to leave whith all the others(everyone of which we presume will think exactly the same)


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