Sentence To Prove Innocent

Logic Level 2

In the court of law, a prisoner is allow to say one sentence to prove he is innocent. He knows that knights tells the truth, knaves tells lies and jokers may tell the truth or lie. However, no one knows his identity. All they know is that he isn't a joker. Out of the following, which of the sentences can prove he is 100% innocent?

  1. A knight committed the crime.
  2. A knave committed the crime.
  3. A joker committed the crime.
2 1 There isn't a sentence that proves he is 100% innocent 3

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2 solutions

Amir Razin
Dec 2, 2018

Assuming he is a knight, Sentence 1 will show he may committed the crime. If he is a knave, Sentence 3 will show that either a knight or a knave did it, which show he may committed the crime. This leaves Sentence 2. If he is a knight, then he cant commit the crime. If he is a knave, then the sentence shows that a knight or joker did it. In either cases he is innocent.

Edit your problem. Is allowed not allow

Hasmik Garyaka - 2 years, 6 months ago
Saya Suka
Apr 26, 2021

The prisoner is forced to speak a sentence that the court will either trust him XOR (exclusive or) accept his innocence, if he wanted to be exonerated. Thus, sentence 2 is the answer.

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