Chapter 1
Expository Articles
1.1. The blue-eyed islanders puzzle
This is one of my favourite logic puzzles. It has a number of formulations,
but I will use this one:
Problem 1.1.1. 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
logical1
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).
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 the island and wins the complete
trust of the tribe.
One evening, he addresses the entire tribe to thank them for their hos-
pitality.
1For
the purposes of this logic puzzle, “highly logical” means that any conclusion that can be
logically deduced from the information and observations available to an islander, will automatically
be known to that islander.
1
http://dx.doi.org/10.1090/mbk/066/01
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