perplexus.info :: Logic : Three More Logicians

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.

Comments: ( You must be logged in to post comments.)

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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