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

Home > Logic > Liars and Knights
A greek guilt (Posted on 2005-09-04) Difficulty: 3 of 5
There was a crime, and it was known that either Al, Beth, Dell, or Phil (each a knight or a liar) was guilty. At the trial, the men spoke first, and said:

Phil: Dell did it.
Al: No, Beth is guilty.

Then it was the ladies' turn, who said:

Beth: Al is lying.
Dell: Phil never lies.

Then a lady accused someone, and that let me know she herself was innocent.

And next the other lady accused someone, and that let me know who was guilty.

Who's guilty?

  Submitted by Federico Kereki    
Rating: 4.0000 (3 votes)
Solution: (Hide)
D accused one of the other three; B accused D; B herself was guilty.

If Al was a knight, then Beth is guilty, and a liar. Phil is lying (since Dell isn't guilty) and Dell is also lying (for she says Phil is a knight).

If Al is a liar, then B is innocent, and a knight (for she says A lies). We have two possibilities: either Dell is a guilty knight and Phil a knight, or both Dell and Phil are liars, and either Al or Dell is guilty. The cases are:

  • A & B knights; D & P liars; B guilty
  • A liar; B & D & P knigths; D guilty
  • A & D & P liars; B knight; A guilty
  • A & D & P liars; B knight; P guilty
  • In the first case, B could have accused A & D & P; in the second, D; in the third, A; and in the fourth, P. No matter whom she accused, I couldn't have decided if she was innocent, so it mustn't have been B the one who talked.

    As to D, in the first case she could have accused A & D & P; in the second, D; in the third, D & P & B, and in the fourth, A & D & B. If she had accused herself, I wouldn't have been able to tell if she was innocent, but if she accused anybody else, then she wasn't guilty. D accused either A or P or B, and the second case didn't occur.

    Now, we know B was the second one who accused someone. If she had accused A or P, I couldn't have told who did it, so it must be the case that she accused D, while being herself guilty.

    Comments: ( You must be logged in to post comments.)
      Subject Author Date
    Some ThoughtsPuzzle Thoughts K Sengupta2023-01-11 00:39:39
    A big question (somehow a flaw)for this problemTerence2005-10-27 06:07:07
    Re: erroneous solutionyao2005-09-09 02:56:10
    Show me my errorjason aaron2005-09-06 20:47:25
    Some Thoughtsre: may be.. something is wrongOld Original Oskar!2005-09-05 12:08:00
    may be..sragen2005-09-05 05:49:12
    The answer, I thinkjason aaron2005-09-05 03:08:24
    a GrEeK gUiLt!!!*mallory2005-09-04 14:48:17
    re: A greek guilt ?Penny2005-09-04 07:05:21
    SolutionA greek guiltPenny2005-09-04 03:33:45
    SolutionI think I have itBasil2005-09-04 02:05:40
    Please log in:
    Login:
    Password:
    Remember me:
    Sign up! | Forgot password


    Search:
    Search body:
    Forums (0)
    Newest Problems
    Random Problem
    FAQ | About This Site
    Site Statistics
    New Comments (3)
    Unsolved Problems
    Top Rated Problems
    This month's top
    Most Commented On

    Chatterbox:
    Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information