All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Who Said What? (Posted on 2007-05-17)
You are in a popular tourist town in the land of Liars and Knights. You happen to overhear a conversation another tourist is having with three of the locals: Alex, Bert and Carl. Each of the three could be a knight, a knave or a liar. You know that for each question the tourist asks, Alex, Bert and Carl each give one response, but you don't know who said what. The conversation is as follows:

1. What type are each of you?
• I am a knight.
• I am a knave.
• I am a liar.
2. How many of you are the same type?
• We are all the same type.
• We are all different types.
• Exactly two of us are the same type.
3. What type is Alex?
• A knave.
• A liar.
• Different from Bert.

Can you determine which type Alex, Bert and Carl are?

 Submitted by Brian Smith Rating: 4.5000 (4 votes) Solution: (Hide) From question 1, the third response must have been given by a knave who lied. The three responses to question 2 all disagree, so only one can be true. The knave who lied in question 1 (claiming to be a liar) must have been the one who told the truth. This also implies that there are no knights. Since there are no knights then there is at most one true response to each question which means that there are either two knaves, with opposing truth patterns and one liar or there are two liars and one knave who lied to the first and third questions. One of the first two responses to question 3 must be true, which means that there are two knaves and one liar. The third response to question 3 is a lie since each question cannot have two true responses. This makes Alex and Bert the two knaves and Carl the liar.

 Subject Author Date Solution Math Man 2011-01-02 12:51:08 solution hoodat 2007-05-17 18:38:21 Comment (part spoiler) Vernon Lewis 2007-05-17 18:14:49 Reasoned out e.g. 2007-05-17 17:52:31 re: solution -- the computer way Charlie 2007-05-17 15:39:39 solution Charlie 2007-05-17 15:36:02 Solution webster726 2007-05-17 14:08:24

 Search: Search body:
Forums (0)