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?

If one of the logicians had the letter C, D or U they would know that the words are CAT it it was C, DRY if it was D or RUN if it was U. Therefore, when they all said no first time that meant neither had any of those three letters.

Of the remaining three words, if either had a T or a A they would know that the word was NET if they had a T or MAN if they had a A. The second time they answered no meant none of them had either of these two letters.

That leaves one word - MEN. Obviously, when they all said yes they all knew they had MEN because it was the only word left.

Posted by Lewis on 2003-06-12 09:24:56