Logic/Induction

[just_you_wait]

Problem: 1000 perfect logicians are imprisoned. 500 have blue eyes, 499 people have brown eyes, and one has green eyes. They can see each other's eyes but not their own, and cannot communicate eye colors to each other. At the end of every day, those who have deduced their own eye color are freed. The guard states, "At least one of you has blue eyes

Comments

[notmrgarrison]

I think this is wrong.

Your assumption that your eyes aren't blue only holds in your head, not the other guys head.

Assume you are one of the blue.
n=1: You can easily tell that you must be it.

n=2: If you're not blue, the other guy should leave, if you're blue, the other guy should stay, so his actions determine your color.

n=3: regardless of what you assume about your own eye color, the other guys will not leave after day 1, so the fact that they don't leave tells you nothing, as you already knew they wouldn't leave (regardless of what your own eye color was). But...

Forget perfect logicians for a moment. Suppose you had the following simple rule: If you see n people with blue eyes and they don't leave after day n, then leave on day n+1. If everyone followed this rule, they (the blue eyed people) would all get it right.

But I'm not convinced perfect logicians would arrive at such a rule, since, if there were 5 blue eyed people, they would know from the beginning of day 1 that regardless of their eye color, no one would leave at the end of the day, so that when no one does, it shouldn't add any information.