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In the land of Twitter, there are two kinds of people: knights (also called outragers), who always tell the truth, and knaves (also called trolls), who always lie. It so happened that a person with handle @anand tweeted something offensive. It was not known whether @anand was knight or a knave. A crack team, headed by Inspector Chitra, rounded up three suspects and interrogated them.

The first interrogation went as follows.

  • Chitra:  What do you know about @anand?
  • Suspect $ 1:$  @anand once claimed that I was a knave.
  • Chitra:  Are you by any chance @anand?
  • Suspect $1:$  Yes.

The second interrogation:

  • Chitra: Have you ever claimed you were @anand?
  • Suspect $2:$ No.
  • Chitra: Did you ever claim you were not @anand?
  • Suspect $2:$ Yes.

The third suspect arrived with a defense lawyer (also on Twitter):

  • Lawyer: My client is indeed a knave, but he is not @anand.
  • Suspect $3:$ My lawyer always tells the truth.

Which of the above suspects are innocent, and which are guilty? Explain your reasoning.

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If Suspect 1 were @anand, then since he answers truthfully to the second question, he is a knight, but then his first reply means that he once claimed he was a knave, which knights will not do. Hence Suspect 1 is not @anand.


If Suspect 2 were @anand, then he is either a knight or a knave. If he were a knight, then the answer to question 2 means he claimed he was not @anand, which is a lie. Hence he is a knave. But then the answer to question 1 is a lie, which means he has once claimed he is @anand, which a liar will not do. This contradiction means that he is not @anand.


Now Suspect 3 cannot be a knight, since he says his lawyer is truthful, and the lawyer says that he is a knave. So Suspect 3 is a knave. And so what he said is false, and his lawyer is a knave. But then the lawyer has uttered a falsehood. Of the conjuction he uttered, at least one conjunct is false.But the first conjunct is true, so the second is false. And Suspect 3 is indeed @anand!

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