Car Thief puzzle

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A rather silly car thief stole, without knowing it, the car of the chief of police. The police immediately started an investigation and based on witness depositions, four suspects were arrested that were seen near the car at the time of the crime.

Because the chief of police took the case very seriously, he decided to examine the suspects personally and use the new lie detector of the police station. Each suspect gave three statements during the examinations, which are listed below:

Suspect A:

“In high school, I was in the same class as suspect C.”
“Suspect B has no driving license.”
“The thief didn’t know that it was the car of the chief of police.”
Suspect B:

“Suspect C is the guilty one.”
“Suspect A is not guilty.”
“I never sat behind the wheel of a car.”
Suspect C:

“I never met suspect A until today.”
“Suspect B is innocent.”
“Suspect D is the guilty one.”
Suspect D:

“Suspect C is innocent.”
“I didn’t do it.”
“Suspect A is the guilty one.”
With so many contradicting statements, the chief of police lost track. To make things worse, it appeared that the lie detector did not quite work yet as it should, because the machine only reported that exactly four of the twelve statements were true, but not which ones.

Who is the car thief ?

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SherlockHolmes Expert Asked on 24th January 2018 in Logic Puzzles.
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  • 2 Answer(s)

    suspect c

    shivashivi Starter Answered on 24th January 2018.

    Why?

    on 24th January 2018.
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    There are 12 statements and only 4 are true. That gives us 495 combinations. I gave the statements the number 1-12 (1-3 to suspect A, 4-6 to suspect B etc.)

    Now i started to eliminate  the combinations that can’t exist:

    Statement  1 & 7 can’t  be both true.  Statement  4 & 9 can’t  be both true. Statement  4 & 12 can’t  be both true.
    Statement  9 & 12 can’t  be both true. Statement 8 can’t be false with statements 4 or 9 or 12 being true .
    Statement 10 can’t be false with statements 9 or 12 being true.
    Statement 10 & 8 can’t be both false
    Statement 11 can’t be false with statement 4 or 12 being true.
    Statement 11 & (5 or 8 or 10) can’t be both false.
    Statement 4 &10  can’t be both  true or both false and so 5 & 12  and 9 & 11.
    If statement 6 is true than B is not the thief.
    If Statements  10 & 11 are true and 12 is false statement 8 can’t be true.

    After all the above i was left with 7 possibilities that gave me all the suspects, i notices that in the beginning of the puzzle, it says that the thief did not know that the car was the car of the chief of police, which means that statement 3 must be true.
    And that fact  leave us with only one option: false, false, true, false, true, false, false, false, false, true, true, false.

    So the thief is Suspect B.

     

    Moshe Curious Answered on 30th January 2020.
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