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Context for the puzzle:

You are on an island inhabited by knights and knaves. Knights always tell the truth, knaves always lie. You meet 5 natives:

  • Carl says "I am the same type as Peter".

  • Zippy says "Carl is a Knave or Jack is a Knight".

  • Jack says "I am a knight and Bill is a Knave".

  • Peter says "Bill is a Knight".

  • Bill says "I am a Knight and so is Carl"

From this, I have formulated the following equivalences:

  1. C ≡ P
  2. Z ≡ ¬C ∨ J
  3. J ≡ J ∧ ¬B
  4. P ≡ B
  5. B ≡ B ∧ C

I am trying to deduce which of the people are knights and which are knaves, however, after doing some substitution and manipulation using logical laws, I get to a point where I cannot make any more simplification and hence get stuck.

Could someone please point me in the right direction towards solving this problem?

Thank you.

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It's not $C ≡ P$ - that would be true in the case of both $C$ and $P$ being knaves. You want $C ≡ (C ≡ P)$, which simplifies to simply $P$.

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  • $\begingroup$ Is ≡ the right symbol here? It feels like we should simply be using =. $\endgroup$ – Dan Uznanski Nov 23 '17 at 12:51
  • $\begingroup$ Thanks for your help. I have reached the conclusion that C,P,B are true and Z,J are false - Carl, Peter and Bill are knights while Zippy and Jack are knaves. Would that be correct? $\endgroup$ – erykkk Nov 23 '17 at 13:12
  • $\begingroup$ Looks right to me. $\endgroup$ – Dan Uznanski Nov 23 '17 at 13:17

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