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Saturday, February 6, 2016

Logic Problem Solved : Truth Tellers and Liars

After such a looong time,I solved a logic problem somewhere on the web.I am not in my best form right now,given the time and situation but solving or reading definitely adds colour to life!

Alice, Bob, Carly, Dave, and Evelyn are taken to the police station for questioning. Detectives know that one of them is the thief and that only one of them tells the truth.

Alice says, "I am not the thief." 
Bob says, "Alice is the thief." 
Carly says, "I am the thief." 
Dave says, "Carly is the thief." 
Evelyn says, "I am not the thief"

Who is the thief?

  • Alice 
  • Bob
  •  Carly 
  • Dave
  •  Evelyn
  •  Insufficient information
Look at the question carefully.There is one,clear certain element in it : There is one truth.Only one.

Start with the elimination method.
If you say Alice is True,it is impossible because then Bob's statement also has to be true but there is only one truth.
Again,if you say the third statement is true,then Dave's statement has to be true,too but that is not possible.The first and last statements are contrapositive.If the first is statement is true,the last one has to be False and if the last statement is true,then the first one has to be False.
If Evelyn is lying,then all the other statements fit.So,Alice is saying the truth.All others are lying.

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  1. Often struggle with these problems
    concentrate to prevent depression taking hold
    as reaction to ease others achieve solutions

    when considering problems self finds easier
    it helps provide understanding with patience
    for those struggling to resolve these...

  2. I can't get it? If Alice is telling the truth Bob's statement has to be true. They are giving completely opposite statemen.

    1. Their statements are opposite.And if Alice is telling the truth,Bob's statement indeed has to be true.That is why,Alice is lying because according to the question,we know that only one has to tell the truth.

    2. WTF? :) I say you are the thief, and you say you are not, and if you are right, I am lying. So this first thing is not correct.
      That logic can apply to Carly and Dave...

  3. This comment has been removed by the author.

  4. Found it elsewhere: "ALice and Evelyn both claim to be innocent, then one of them is the thief. If Evelyn is innocent and telling the truth, then Alice would be the thief. However, then Bob would also be telling the truth, which contradicts that there is only one person telling the truth.Thus, Evelyn must be guilty (and lying, whereas Alice is telling the truth and Bob/Carly/Dave are lying)."

    1. That's the result I came up with and yet there are so many other answers down here.
      But after all I still think Evelyn is the culprit.

    2. That's the result I came up with and yet there are so many other answers down here.
      But after all I still think Evelyn is the culprit.

    3. Use the elimination method and there IS only one,single answer you'll find!

  5. I would say if you know how to solve a hard sudoku puzzle, you will know how to solve such puzzles which requires the method of elimination.

    1. :) That's a great analogy.And these are better than detective stories,often.


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