How many knights are there?

Question

I cannot deduce the solution. I cannot deduce a solution. Consider the case in which Anne is a Knave. If Anne answers "Yes", then they are not both knights. Berne might be a knight, or they might be a knave. If Anne answers "No", then they are both knights. But Anne is a knave, so this leads to a contradiction. Therefore if Anne is a Knave, she answers "Yes", and Berne is either a Knight or Knave.

Consider the case in which Anne is a Knight. "Yes" indicates they're both knights. "No" indicates that Berne is a "Knave".

An answer of "No" thus indicates one knight. An answer of Yes indicates 2 Knights, 1 Knight, or 0 Knights.

This question can only be solved if Anne answered "No". But we are not given Anne's answer. As such we cannot discriminate between the options.

Answer 1

Consider the case in which Anne is a Knave. If Anne answers "Yes", then they are not both knights.

Anne is lying, so it could be that either Bernie is a knight and she is a knave or they are both knaves.

If Anne answers "No", then they are both knights. But Anne is a knave, so this leads to a contradiction.

Yup, so that will never happen. So if she responds "No" she is a knight and Bernie is a knave.

In essence, if she responds yes there is no way to tell how many there are. Thus, she responded "No". So there is 1 kinght and 1 knave.