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 the word were CAT, DRY or RUN, the person with the C or the U, or the two with D and Y would have announced he knew the word right away, as there is only one of each of these letters in all the words.

If the word were NET, the logician with the T would, after the first round, know that the word was not CAT, and so must be NET as there are only 2 A's, and announce such on round 2. Likewise, if the word were MAN, the logician with the A would also know that the word isn't CAT, and announce MAN on round 2.

Now everyone knows that the word must be MEN, as any other word would have been guessed in round 1 or round 2.

or MAN, the logicians, knowing about what was said in the first paragraph here,

Posted by Charlie on 2003-06-12 08:58:01