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.

July 2, 2009 pm31 11:27 pm 11:27 pm

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

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. July 3, 2009 pm31 5:52 pm 5:52 pm

Proposed solution moved to: https://jd2718.wordpress.com/2009/07/03/responses-to-multiple-pov-logic-puzzles/#comment-43728

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.

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

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.