I ran into this logic puzzle and have been working on it for couple hours now but i cant seem to explain clearly why the answer i came up with is the answer. Heres the question: The police have three suspects for the murder of Mr. Cooper: Smith, Jones, and Williams. Smith, Jones, and Williams each declare that they did not kill Cooper. Smith also states that Cooper was a friend of Jones and that Williams disliked him. Jones also states that he did not know Cooper and that he was out of town the day Cooper was killed. Williams also states that he saw both Smith and Jones with Cooper the day of the killing and that either Smith or Jones must have killed him. Cna you determine who the murderer was if a) 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? b) innocent men do not lie? For (a) Well, this is what i think (im not too good with p->q, this kinda stuff and can only say it in plain words). assuming smith is innocent and telling the truth, this means that jones is a friend of cooper and williams disliked cooper. this also means that jones ied by saying he does not know cooper and that he was not with cooper on the day of murder. Since two innocent men are telling the truth, and have determined that jones lied (assuming smith is telling the truth), then williams also must be telling the truth. This means that jones was with cooper and either jones or smith killed him. Since smith is innocent, then jones is guilty. Asuuming that Mr wiliams is innocent and is telling the truth, then both smith and jones was with cooper and either smith or jones must have killed him. If this is the case, then jones lied by saying he was out of town on the day of murder and he did not know cooper. Then this makes smith's statement that jones was a friend of cooper. Therefore jones is the murderer. For (b) I said you cannot really determine for sure, because you can have multiple murderers. Just like case question a above, if there's only one murderer, then its jones; however the question doesnt explictly say that so there can me multiple murderers. This means that if jones is innocent, then both smith and williams is lying therefore they are both murderers. also all three can be lying that they all could be murderers. Im not sure if im thinking this correctly but this is what i came up with and if someone could verify this question for me i'd be really really thankful. thanks in advance.