Knight or Knave? - 1

Level 1

There are three persons A , B and C , each a knight or a knave. A and B make the following statements:

A : "All of us are knaves."

B : "Exactly one of us is a knight."

What is C , a knight, or a knave?

Details and Assumptions:

A knight is a person who always speaks the truth & a knave always speaks lies.

This problem is the part of my set Is This What You Call Logic?!

Information insufficient Knave Knight I can't work it out!

Ameya Salankar by Ameya Salankar , 23, India

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3 solutions

Abhay Tiwari
Jul 13, 2015

A: all of us are knaves. If A is a Knight, then he is speaking truth.But his statement is saying for all to be knave.So, this does not satisfy.Definitely, he is a knave. Now, B: exactly one of us is a KNIGHT. Now since A is a knave so his statement is false, that means the remaining two B and C can be knight or 1 of them can be knight. Now considering B's statement. If B is a knave then his statement is false. But it is contradicting with A's statement. So, B is a knight and therefore what he is saying is truth. And since only one is a knight the remaining one i.e. C is definitely a KNAVE.....!! CAUGHT THE CULPRIT... :)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ansh Bhatt
Mar 3, 2015

First of all, A can not be a knight as than his statement would become false, which is not possible, so A is a knave and thus there is at least one knight. B cannot be a knave as then his statement would become true, which again is not possible, so B is a knight and according to his statement, which of course is true, C cannot be a knight. Thus C is a knave.

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The question never specifies that there has to be at least one knight and one knavewhich leaves it as anybody's guess as to what C is.

Palmer Feinberg - 6 years ago

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The first statement implies that there is at least one knight, because stating "All of us are knaves" is something a knight cannot say, because that would be a lie, and the fact that a knave said it implies that the three of them can't all be knaves, because that would make the statement true.

Tristan Goodman - 1 year, 2 months ago
Saya Suka
Apr 25, 2021

By claiming that all of them are knaves, A could not have been a Knight but as the statement is a lie, therefore at least one of the others must be a Knight. B's statement of "only 1 Knight" to either be true, or both of B & C to be Knights. Either way, B is a Knight so by his / her true statement, B is the sole Knight among the three. C can only be knave as a result.

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