# Knight and Knave problem with 3 people.

A says "All of us are Knaves".

B says "Exactly one of us is a Knight".

C says Nothing.

In this problem the right solution we get from A and B will be the answer ?

I get that A is Knave, B is Knight and C is Knave from A as Knave and B as Knight. Will this be the right answer ?

• All knights are knaves. I don't support nobility myself. – Mortified Through Math May 6 '17 at 21:42

A cannot be a knight, for then they would all be knaves, including A.

So, A is a knave.

That means that they are not all knaves, and so at least one of B and C is a knight.

So, if B would also be a knave, then C is a knight ... the only knight ... so B is telling the truth ... which doesn't work. So: B is a knight.

Which means that there is exactly one knight, and hence C is a knave.

So yes: A is a knave, B is a knight, and C is a knave.

• @Student28 You're welcome :) – Bram28 May 7 '17 at 11:25

I agree. A is a Knave. B is a Knight. C is a Knave.

You can make a truth table or formalize the statements.

A: ~A & ~B & ~C

B: (A&~B&~C) OR (~A&B&~C) OR (~A&~B&C)

The question is similar to A saying that everybody is a liar. Then he is a liar himself because B is telling the truth and C is lying without saying anything.