A waiter approaches a table where there are three logicians and asks them: “Do you three want beer?” The first one answers:
“I don't know.” The second answers:
“I don't know.” The third answers:
“Yes.” Why can you say this with certainty?
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The three logical in the bar
One of the cleanest scenes in common knowledge: three minimal answers, each adding exactly the information that was missing.
Hints
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- If either of the first two didn't want beer, they could have responded immediately.
- The first, by saying “I don't know,” reveals something about himself.
- The third person hears the two previous answers and also knows what he himself wants.
Solution
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If the first one didn't want beer, he would know immediately that the answer to "Do all three of you want beer?" It's no, and I would have said it. Since he answers “I don't know,” that means he does want beer, but he doesn't know what the other two want.
The second hears that answer. If he didn't want beer, he could also immediately answer “no,” because he would already know that not all three of them want beer.
Since he also answers “I don't know,” that means he wants beer too. The third person hears both answers and also knows that he himself wants beer.
So you can now conclude that the first wants beer, the second wants beer and so does he.
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