The police have three suspects for the murder of Mr. Morgan: Mr. Hill, Mr. Spengler, and Mr.Gates. Hill, Spengler, and Gates each declare that they did not kill Morgan. Hill also states that Morgan was a friend of Spengler and that Gates disliked him. Spengler also states that he did not know Morgan and that he was out of town the day Morgan was killed. Gates also states that he saw both Hill and Spengler with Morgan the day of the killing and that either Hill or Spengler must have killed him. Can you determine who the murderer was if one of the three men is guilty, the two innocent men are telling the truth, but the statements of the guilty man may or may not be true?
I think that
Spengler is the murderer. Because if he's speaking the truth then that would mean he was out of town and didn't know Morgan. That would negate both Hill (Hill said Spengler was a friend of Morgan) and Gates (Gates said he saw Morgan with Spengler the day he was murdered). However, we know that at least two of the suspects are speaking the truth, so Spengler must be the liar and hence the murderer.
If Gates is telling the truth about seeing Morgan and Spengler together, then Spengler must be lying about not knowing the deceased.
If Hill is telling the truth about Morgan and Spengler being friends, then Spengler must be lying about not knowing the deceased.
If only the murderer is lying then at least one of Gates and Hill must be truthful, but if either is truthful then, Spengler must be the murderer.