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?

MEN

I am assuming that the men can see the list of possible words, or else the problem does not make sense. Also, I assume they can hear everyone's answers for the previous questions..

If any of the men had a C, D, Y, or U, they would know right away since each of those letters appears in only one word.
Since no one guesses it right away, they know that the word is not CAT, DRY, or RUN.

The remaining words are, then, NET, MEN, or MAN.
At this point, a logician with a T or an A will know right away what the word is after the first answer, since they each appear in only one of the remaining words.

Since no one guessed it the second time around, none of them had either T or A, and the word is not NET or MAN.
Therefore, the three letters are E, M, and N, spelling MEN.

Posted by DJ on 2003-06-12 11:47:29