Puzzle #165: Truth & Lies – 7 of them!

Welcome back, and a very happy new year to all of you. Lets start with a new puzzle before I post solutions to previous problems. I will begin this week with a very nice puzzle from the NSA collection.

Here it goes:

The chief detective hurried down to the police station after hearing big news: there was a heist at Pi National Bank! The police had brought in seven known gang members seen leaving the scene of the crime. They belonged to the nefarious True/False Gang, so named because each member is either required to always tell the truth or required to always lie, although everyone is capable of engaging in wrongdoing. The chief also knew from his past cases that any crime committed by the gang always included one truth teller.

When the chief showed up, he asked the gang members the following questions:

  • 1) Are you guilty?
  • 2) How many of the seven of you are guilty?
  • 3) How many of the seven of you tell the truth?

Here were their responses:

  • Person 1: Yes; 1; 1
  • Person 2: Yes; 3; 3
  • Person 3: No; 2; 2
  • Person 4: No; 4; 1
  • Person 5: No; 3; 3
  • Person 6: No; 3; 3
  • Person 7: Yes; 2; 2

After looking these answers over, the chief prepared to arrest those responsible.

Which of these seven did the chief arrest?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy policing!

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3 Responses to Puzzle #165: Truth & Lies – 7 of them!

  1. Abhinav Jain says:

    Person 2,5,6 are the truth tellers.
    The chief should arrest person 2,3 and 4

  2. Vishal Poddar says:

    There can be 1,2 or 3 truth tellers as the person saying truth will give the correct answer to question 3.

    Case 1 truth teller – 2 of them claimed 1 truth teller, not possible.
    Case 2 truth teller – Person 3 and 7 will be truthful, both of them saying 2 people guilty, but seeing to answer of question 1 it seems that there would be 3 people guilty.
    Case 3 truth teller – Person 2,5 and 6 will be truthful. 3 people will be guilty, so Person 2, 3 and 4 are guilty and will be arrested.

  3. Either Persons 2,5,6 tell the truth, or Persons 3,7 tell the truth, or Person 1 tells the truth, or Person 4 tells the truth

    4 cases:
    – Persons 2,5,6 tell the truth – So 3 tell the truth – 3 are guilty. Persons 2,3,4 are guilty. This is consistent.
    – Persons 3,7 tell the truth – So 2 tell the truth – 2 are guilty. Persons 4,5,6,7 are guilty. Inconsistent.
    – Person 1 tells the truth – So 1 tells truth – 1 is guilty. Persons 1, 3,4,5,6 are guilty. Inconsistent.
    – Person 4 tells the truth – So 1 tells truth – 4 are guilty. Persons 3,5,6 are guilty. Inconsistent.

    So, the chief arrested Persons 2,3,4 .

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