Wednesday, February 06, 2008

The blue-eyed islanders puzzle

The morning pill: Terry Tao has just reminded me of the following famous logic puzzle. Obviously some of you have seen it before and might know the answer (disclaimer: I was confronted with this quite a while ago, in my first university year, as part of a challenge among Maths students), but many of you did not. Try to think about it on your own before checking the web for answers :-). Here's the puzzle in Tao's formulation:

There is an island upon which a tribe resides. The tribe consists of 1000 people, 100 of which are blue-eyed and 900 of which are brown-eyed. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and highly devout, and they all know that each other is also highly logical and highly devout.

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?

If you give up (don't!) or simply want to check your reasoning, read Terry Tao's entire post and the subsequent comments. And if you still have problems understanding, you're welcome to drop a line :-).

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