A logician named John went to the Land of Knights and Liars. He met two inhabitants, A and B. He asked A two questions.
John:Has B ever said that you are a liar?
A answered, either "Yes" or "No."
John:Is B a liar?
A answered, either "Yes" or "No."
The next day, another logician named Jack went to the Land of Knights and Liars. He met the same two inhabitants, A and B. He also asked A two questions.
Jack:Has B ever said that you are both liars?
A answered, either "Yes" or "No."
Jack:Is B a liar?
A answered, either "Yes" or "No."
One of the two logicians, John and Jack, could figure out what types A and B were, but the other logician could not figure out their types. What are A and B?
So, I got the right answer, but made some mistakes which mean that my reasoning was not quite right. Let's try all over again.
There are a few cases:
1) B is a Knight and said nothing about A
2) B is a Knight and A is a liar and B said so
3) B is a Liar and he said nothing about A
4) B is a liar and A is a Knight and B called A liar
5) B is a liar and A is a Knight and B called them both liars
Then the Answer table is as follows:
Row A B B said Q1 Q2 Q3 Q4
--- - - ----------- -- -- -- --
1 K K 1) Nothing N N N N
2 K L 3) Nothing N Y N Y
3 K L 4) A lies Y Y N Y
4 K L 5) We both lie Y Y Y Y
5 L K 1) Nothing Y Y Y Y
6 L K 2) A lies N Y Y Y
7 L L 3) Nothing Y N Y N
John can only work it out if he gets a N N or a Y N (rows 1 or 7)
Jack can only work it out if he gets a Y N or a N Y or a N N (rows 1, 2, 3, or 7)
The only rows where one logician can work it out and the other cannot are rows 2 and 3.
So, A is a Knight and B is a liar. We don't know if B ever said that A lies, but we know that he never said that they both lie.
Second attempt
