How many knights are there? 
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.


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.
