3 ms·

The blue-eyed islanders puzzle

• tromp 5y ago
  Solution 1 is wrong, because it fails to consider transitive knowledge. This is seen most clearly if n were only 3 instead of 100. Then everyone in the tribe can already see that n >= 2. Yet what they didn't know before the public announcement is that everyone knows that n >= 2. If I'm one of the 3 blue-eyed islanders, then I didn't know that the other 2 blue-eyed islanders know that n >= 2. So everybody learns something new. The fact that it's transitive knowledge just obscures things, especially when n is as large as 100. The foreigner has no effect, because his comments do not tell the tribe anything that they do not already know (everyone in the tribe can already see that there are several blue-eyed people in their tribe).