Knight, Knave and Spy in a Conversation

Logic Level 2

Knight: Always tells the truth.

Knave: Always tells a lie.

Spy: Sometimes tells the truth and sometimes lies.

Consider this conversation between a knight, a knave, and a spy (who know who is which):

Alice: Bob always lies.

Bob: Alice just lied.

Alice: I always lie.

Charlie: I don't lie.

Bob: Charlie, that is not true.

Alice: Charlie never lies though.

Charlie: Bob, we both know, that Alice doesn't lie.

Who is the knight?

Alice Bob Charlie Not Enough Information Impossible Case

Ron Lauterbach by Ron Lauterbach , 18, Germany

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2 solutions

Kenny O.
Sep 18, 2017

As there is only 1 knight, a knight who not say that another person would not ever lie. This eliminates Alice and Charlie, meaning Bob is the Knight.

2 Helpful 1 Interesting 1 Brilliant 0 Confused

Alice can’t be a knight because knights can’t lie and say that they always lie because then that would cause a contradiction. But Alice can’t be a knave either because knaves can’t tell the truth and admit that they always lie because then that would also cause a contradiction. This means that Alice is the spy. So since Alice is the spy and Bob is the knight, this leaves Charlie as the knave.

Diana Bradish - 1 year, 1 month ago
Saya Suka
Feb 8, 2021

Alice's "I always lie" statement is unique to spies. As such, Charlie's "Bob, we both know, that Alice doesn't lie" must be a lie, since Alice occasionally lies as a spy, and thus Charlie must be a knave, leaving Bob to be the Knight.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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