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Given that there has recently been a lot of discussion on this blog about this logic puzzle, I thought I would make a dedicated post for it (and move all the previous comments to this post). The text here is adapted from an earlier web page of mine from a few years back.

The puzzle has a number of formulations, but I will use this one:

There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. 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 or her 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 devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).

[Added, Feb 15: for the purposes of this logic puzzle, “highly logical” means that any conclusion that can logically deduced from the information and observations available to an islander, will automatically be known to that islander.]

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

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?

The interesting thing about this puzzle is that there are two quite plausible arguments here, which give opposing conclusions:

[Note: if you have not seen the puzzle before, I recommend thinking about it first before clicking ahead.]

I gave a non-technical talk today to the local chapter of the Pi Mu Epsilon society here at UCLA. I chose to talk on the cosmic distance ladder – the hierarchy of rather clever (yet surprisingly elementary) mathematical methods that astronomers use to indirectly measure very large distances, such as the distance to planets, nearby stars, or distant stars. This ladder was really started by the ancient Greeks, who used it to measure the size and relative locations of the Earth, Sun and Moon to reasonable accuracy, and then continued by Copernicus, Brahe and Kepler who then measured distances to the planets, and in the modern era to stars, galaxies, and (very recently) to the scale of the universe itself. It’s a great testament to the power of indirect measurement, and to the use of mathematics to cleverly augment observation.

For this (rather graphics-intensive) talk, I used Powerpoint for the first time; the slides (which are rather large – 3 megabytes) – can be downloaded here. [I gave an earlier version of this talk in Australia last year in a plainer PDF format, and had to get someone to convert it for me.]

[Update, May 31: In case the powerpoint file is too large or unreadable, I also have my older PDF version of the talk, which omits all the graphics.]

[Update, July 1 2008: John Hutchinson has made some computations to accompany these slides, which can be found at this page.]