D walks into a room and sees his computer is broken. He asks "Who broke my computer?".
A says B did it
B says A is lying
C says he did not
Of the three, it is known that only one is trustworthy and the other two always lie.
Can this be solved?
A quick logical analysis of the 3 statements reveals that
C did it, and B is the one telling the truth.
If A were telling the truth,
B must have done it, B is lying (ok), and C has to be lying, meaning he also did it (not ok).
If C were telling the truth,
A is lying and B did not do it, and B is lying so A told the truth (contradiction).
B is the only one who can be telling the truth, A is lying because B did not do it, and C is lying because he did it.
A slightly shorter solution, assuming only 1 person did it:
B says A is lying. If that's false, A is telling the truth, otherwise, B is telling the truth. Eitherway, C is lying, and must have done it.
I will add another solution
C is telling the truth
B is lying, his sentence become "A is telling the truth"
The important point is that it is not an absolute truth but just B thinking A is telling the truth, it just implies a thought
A is lying, so B did no break it
A broke it.