perplexus.info :: Liars and Knights : The blurred note

The blurred note (Posted on 2007-04-10)

You get a note from the police station. Unfortunately, it is full of coffee stains.

We have tracked down three suspects for a murder. We know that one of them is guilty and each one of them can be either a knight or a liar. Each one of them wrote a statement or two, but parts of them are full of coffee stains and we are not sure which one of the words in the brackets should be under each coffee stain:

A: ███ (B/C) is innocent. He is also a knight.

B: A is █████ (innocent/guilty). He is also a liar

C: A and B are both ████ (liars/knights)

From these statements, can you figure out who is guilty?

See The Solution Submitted by Assaf

Rating: 4.0000 (4 votes)

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Explanation for Puzzle Answer

Comment 8 of 8 |

(In reply to answer by K Sengupta)

If B is a liar, then in terms of his false statement A must be a knight.

If B is a knight, them in terms of his true statement, A must be a liar.

Accordingly, it follows that A and B must belong to different types.

However, C's statement suggests that A and B belong to the same type. Therefore, C must be a liar.

Hence, there are precisely one knight and two liars.

In such a situation, if A's statement is directed at C stating that C is a knight, then we observe it is a false statement.

Similarly, if A's statement directed at B is true, then both A and B are knights. Contradiction.

Therefore, A is a liar, so that B must be a knight.

Now, A's statement cannot concern B since in such a situation his statement about B's type would be truthful.

Accordingly, A's statement must involve C and the statement "C must be innocent" must be false, since A is a liar.

Consequently, C is guilty.

Then, summarizing, we have:

A is a liar

B is a knight

C is a liar

C is guilty.

Edited on March 21, 2022, 1:37 am

Posted by K Sengupta on 2022-03-21 01:34:20

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