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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?

 Submitted by Gamer Rating: 4.4000 (5 votes) Solution: (Hide) After they all no, all three know that it can't be CAT, DRY or RUN, because no other word contains C, Y, D or U. One of them would have had to have said "Yes" for it to be one of these words. Then, NET, MEN, and MAN are the only words that remain. Since they all said no, nobody could have had a T or an A because they only occur once in the reduced word list. This means NET and MAN are eliminated, leaving MEN to be the only word left. Since MEN is the only word left, all three know which word it is.

 Subject Author Date Answer K Sengupta 2008-10-12 04:50:37 Lol gabbo 2004-09-15 23:11:29 Solution nikki 2003-06-13 14:28:43 Solution DJ 2003-06-12 11:47:29 Solution Lewis 2003-06-12 09:24:56 solution Charlie 2003-06-12 08:58:01

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