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?
(In reply to
With a little interpretation (spoiler) by Steve Herman)
You got the correct answer. However, your tables are a little off. If the first table of "obvious" answers assumes that B has said that A is a liar if B can say it, then there is a mistake. If A is a liar and B is a knight, then B can say that A is a liar, so A would say, "No" to John's first question. Therefore, the table should be this.
A B Q1 Q2 Q3 Q4
- - -- -- -- --
K K N N N N
K L Y Y Y Y
L K N Y Y Y
L L Y N Y N
Of course, just because B can say that A is a liar does not mean that B did say it. However, the rest of the table agrees with that interpretation. Is that what you meant?
Similarly, for the second table, if B has said that A is a liar if B can say it, but B has never said that they are both liars, then the answer to Q1 in the LK case should be an N.
A B Q1 Q2 Q3 Q4
- - -- -- -- --
K K N N N N
K L Y Y N Y
L K N Y Y Y
L L Y N Y N
However, really, just because B can say something does not mean that B has said it. Therefore, A can say, "Yes" or "No" to Q1 if A and B are of different types. Also, A can say "Yes" or "No" to Q3 if A is a knight and B is a liar. Therefore, the correct table looks like this.
A B Q1 Q2 Q3 Q4
- - -- -- -- --
K K N N N N
K L Y, N Y Y, N Y
L K Y, N Y Y Y
L L Y N Y N
The solution is still the same. A is a knight and B is a liar. John either received the answers Yes, Yes, or No, Yes. He could not figure out their types. Jack received the answers No, Yes. He figured out that A is a knight and B is a liar, but B never said that they were both liars.
Edited on July 11, 2024, 8:43 pm
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Posted by Math Man
on 2024-07-11 17:50:44 |
re: With a little interpretation (spoiler)
