Who Is The Thief? 3 Suspects

Logic Level 1

Alice, Bob, and Chris 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."
Chris says, "I am not the thief."

Who is the thief?

Alice Bob Chris

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Gabe Smith by Gabe Smith , 26, USA

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6 solutions

Mariana C
Jul 3, 2016
Alice T F F
Bob F T F
Chris F F T
  1. If Alice is telling the truth, then Chris is the thief.
  2. If Bob is telling the truth, well, it is impossible because Chris would be telling the truth too.
  3. If Chris is telling the truth, then Alice must be lying, and she must be the thief. But this is impossible, because then Bob would be telling the truth too.

So, Chris is the thief.

8 Helpful 0 Interesting 0 Brilliant 1 Confused

The answer is represented quite simple and good. Its nice to show them in tables!

Akhash Raja Raam - 4 years, 11 months ago

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Nice to know, it's my first solution here! Thanks.

Mariana C - 4 years, 11 months ago
Gabe Smith
Jun 23, 2016

Relevant wiki: Truth-Tellers and Liars

There is only one truth teller, but Alice and Chris both claim to be innocent, so one of them must be the thief.

If Chris 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, Chris must be guilty (and lying, whereas Alice is telling the truth and Bob is lying).

4 Helpful 0 Interesting 0 Brilliant 1 Confused

If Chris is answer, then Aice is also telling truth, which contradict the answer. Question is incorrect.

Ashwini Kumar - 4 years, 10 months ago

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Alice is telling the truth and Chris is the thief. There's nothing wrong there. Chris is lying.

Kenneth Choo - 4 years, 10 months ago

if only one is a thief, then there should be two truth tellers i guess

Jaycob Clavel - 4 years, 8 months ago

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The problem has already stated that only one of them tells the truth. If there are two truth-tellers the answer cannot be determined.

Kenneth Choo - 4 years, 8 months ago
Owen Berendes
Aug 3, 2016

Statements one and two are contradictory so one of them is true and the other false. The only solution which will yield 2 false statements and one true statement is to force the third statement to be false, therefore Chris must be the thief.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Jamie Nephew
Sep 24, 2016

Bob accuses Alice, Alice defends herself. No one mentioned it to Chris, so why is he feeling the need to defend himself?... Shows his guilt

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Aura Odum
Sep 5, 2016

true == 1

if Alice = thief

  • alice.statement = false
  • bob.statement = true
  • chris.statement = true

true = 2 /error

if Bob = thief

  • alice.statement = true
  • bob.statement = false
  • chris.statement = true

true = 2 /error

if Chris = thief

  • alice.statement = true
  • bob.statement = false
  • chris.statement = false

true = 1 /valid

answer: Chris

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Audrey Papke
Aug 26, 2016

Bob and Chris, Jeff and cops, are in cahoots.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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