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Who Said What? (Posted on 2007-05-17) Difficulty: 3 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2011-01-02 12:51:08
Solutionsolutionhoodat2007-05-17 18:38:21
Comment (part spoiler)Vernon Lewis2007-05-17 18:14:49
SolutionReasoned oute.g.2007-05-17 17:52:31
Solutionre: solution -- the computer wayCharlie2007-05-17 15:39:39
SolutionsolutionCharlie2007-05-17 15:36:02
Solutionwebster7262007-05-17 14:08:24
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