# Who broke it. 3 person logic

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?

• "C says he did not." Who does that he referring to? is it himself (C)? – athin Feb 20 '18 at 3:48
• C is saying he most certainly did not break it – Jayc Feb 20 '18 at 3:49
• Do we know how many (if any) of the statements are true? Do we know if any of the three (A, B, and C) usually tell the truth (or usually lie)? – puzzledPig Feb 20 '18 at 3:56
• It cannot be solved. The Question is unclear. you have to tell us how many liars there. – Jamal Senjaya Feb 20 '18 at 3:56
• My bad. Of the three, it is known that only one is trustworthy and the other two always lie. – Jayc Feb 20 '18 at 3:57

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).

Therefore,

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.

• Instead of relying on the logical contradiction, you could say that if C told the truth, then A is lying, confirming B's statement (that A is lying), resulting in 2 truth tellers where we know there's only 1. – Lawrence Feb 20 '18 at 9:45
• @Lawrence: admittedly, the accepted answer is not the most elegant way of proving the result, but hey! Green tick! – Xenocacia Feb 20 '18 at 9:57
• Haha - congratulations. :) – Lawrence Feb 20 '18 at 10:34

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.

C is telling the truth

That implied

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

And

A is lying, so B did no break it

Therefore,

A broke it.

• Maybe downvoters could comment and point out the mistake. Read the second spoiler tag, that's the important point of my reasoning. – Saeïdryl Mar 8 '18 at 10:08