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 Three More Logicians (Posted on 2003-06-12)
The three logicians are back. Just like before, they are given each a letter, so that nobody has the same letter, each logician can only see his own letter, and so that their letters can form one of the following words:

NET, CAT, MEN, DRY, MAN, RUN

They answer "Do you know which word can be spelled by your letters?" again, but this time say their answers at the same time, such that they can hear everyone's answers for the following questions, but not for the current one.

First time: All say No.
Second time: All say No.
Third time: All say Yes.

What word do their letters spell?

 See The Solution Submitted by Gamer Rating: 4.4000 (5 votes)

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 Solution | Comment 4 of 6 |
I haven't read the other posted solutions, so maybe mine is just a boring repeat.

The word is MEN.

After the first time they all answer, we know none of the logicians have C, D, Y or U. There is only one word that has one of those letters in them, so if one of them had C, D, Y or U then they would know the word on the first cycle.

Before they all answer the second time, everyone knows that noone knew the word yet, so they rule out Cat, Dry, and Run. Following the same idea, after they answer we know none of the logicians have T or A because now there is only one word that has one of those letters in them (after removing the previously mentioned words).

So at the beginning of the third cycle, the logicians have already removed Net and Man from the list, so the only word left is MEN so now they can all say yes at the same time.

Question: How is the "they all answer at once and need 3 tries to know the word" concept any different than if they each answered individually and the result was "Logician A: No, Logician B: No, Logician A: Yes"? It's the same idea.
 Posted by nikki on 2003-06-13 14:28:43

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