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The case with 3 people always bugs me in solutions for this puzzle: If Alice, Bob, and Carol have blue eyes how can they not know that everyone knows that ther
by ckuehne 16y ago
The case with 3 people always bugs me in solutions for this puzzle:
If Alice, Bob, and Carol have blue eyes how can they not know that everyone knows that there are blue eyed people?
- lkozma 16y agoThey know that everyone knows that there are blue eyed people. What they don't know is that everyone knows this. In other words, they don't know that everyone knows that everyone knows that there are blue eyed people. Alice thinks like this: 1. there are blue eyed people (e.g. Bob and Carol) 2. everyone knows there are blue eyed people (Bob can see Carol, Carol can see Bob, everyone else can see them) 3. I know that 2 is true, but Bob and Carol might not know. Bob might think that Carol thinks that there are no blue-eyed people. (Of course, in reality, Bob does not think this because he can see Alice as well)
- ckuehne 16y agoThanks. That was very helpful. Its easy to see but somehow hard to believe that this applies to 4 people as well (now everyone can see 3 blue eyed people) etc.
- deleted 16y ago[deleted]