Jeremy was killed.
Peter claims that Tom is guilty.
Tom says that Ralph is guilty.
John swears he didn't kill Jeremy.
Ralph says that Tom is lying.
If only one person is telling the truth, then:
Who killed Jeremy?
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$\begingroup$ @MechMK1 Next time i will make it for you $\endgroup$– rudraNov 27, 2017 at 9:18
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$\begingroup$ I'm sorry if my comment came off as rude. I was more genuinely interested if this outcome is always the case or if it has just been a coincidence on my part $\endgroup$– MechMK1Nov 27, 2017 at 9:22
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$\begingroup$ @MechMK1 never mind just jave fun $\endgroup$– rudraNov 27, 2017 at 9:23
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1$\begingroup$ @Silverfish Ralph is the one who says the truth, so he could accuse anyone of lying, or accuse Johhn of being the murderer. He is a bit of a special case $\endgroup$– MechMK1Nov 27, 2017 at 10:21
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1$\begingroup$ Lots of complicated answers here. But it is simple: If John is telling the truth, everybody else is lying, but Ralph is saying one of the others is lying (i.e. he is telling the truth): contradiction. Therefore John is not telling the truth. $\endgroup$– JeremyPNov 28, 2017 at 10:12
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7 Answers
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Making the important assumption that only one person committed the murder, it must have been:
John.
If Peter told the truth, by virtue of the stipulation that only one person is telling the truth, that means that Tom and Ralph are both lying. But Ralph said that Tom is lying, so he would be telling the truth, so Peter cannot be the truth teller.
If Tom told the truth, John's claim that he didn't kill Jeremy is a lie, but Tom said that Ralph was guilty. Both of them can't be true at once, so Tom can't be the truth teller.
If John is telling the truth, then Tom is lying about Ralph being guilty, but Ralph says that Tom is lying, which would be true. So, John cannot be telling the truth.
By the process of elimination, we can conclude that Ralph is telling the truth that Tom is lying. Thus, John is lying, and must have killed Jeremy.
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$\begingroup$ Is the assumption here that everyone is aware of the actual murderer? $\endgroup$ Nov 27, 2017 at 16:17
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1$\begingroup$ For a puzzle labeled only as 'liars', I think it necessarily is. If the person isn't aware and they say something that isn't true, that doesn't mean they're lying, it's just false. It's an extra layer of complexity that could make for a more interesting puzzle, but it isn't the format that's expected here. Incidentally, I'm not sure how well it works to have merely 'false' statements in this setting, where the characters are literally accusing each other of murder! $\endgroup$– user42669Nov 27, 2017 at 18:56
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$\begingroup$ Your assumption is not really necessary - because even if Ralph "is guilty", John is lying in both possible solutions, and the negation of his statement clearly sets him as the murderer. So without assumptions the solution is "John is the murderer and maybe Ralph is guilty too" $\endgroup$– FalcoNov 28, 2017 at 9:46
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A slightly faster explanation of why
John is guilty
Since
Ralph says that Tom is lying,
The one person who says the truth is
either Ralph or Tom
As a consequence
John lies. But John swears he didn't kill Jeremy, hence he did it.
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The killer is:
John
Reason: Because only one statement can be true:
- Peter claims that Tom is guilty.
- Tom says that Ralph is guilty.
- John swears he didn't kill Jeremy.
- Ralph says that Tom is lying.
If 1 is true:
makes 4 true as well
If 2 is true:
makes 4th true as well
If 3 is true:
then makes conflict in 2 and 4 either of them is true
If 4 is true:
makes john guilty as all other statements are false
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3$\begingroup$ Maybe you did, but you won the formatting war. ;) Even with the previous edit a kind soul made on my previous answer to help guide me, I still can't figure out how to get these miserable spoiler tags to work. $\endgroup$– user42669Nov 27, 2017 at 4:42
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$\begingroup$ @JamesGryphon you just need to enter new lines(just press enter) before and after spoiler line $\endgroup$– PreetNov 27, 2017 at 4:45
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The killer MUST be either Peter, Tom, Ralph, or John. In the case that the killer is not one of them,
both John and Ralph would be telling the truth.
With that in mind, the killer must be
John
My thought process:
If Peter is Guilty
-Peter is lying, because Tom is innocent
-Tom is lying, because Ralph is innocent
-John is telling the truth, because he is innocent
-Ralph is telling the truth, because Tom is lying
Two people are telling the truth, so therefore Peter cannot be guilty.
If Tom is Guilty
-Peter is telling the truth, because Tom is guilty
-Tom is lying, because Ralph is innocent
-John is telling the truth, because he is innocent
-Ralph is telling the truth, because Tom is lying
Three people are telling the truth, so therefore Tom cannot be guilty.
If John is Guilty
-Peter is lying, because Tom is innocent
-Tom is lying, because Ralph is innocent
-John is lying, because he is guilty
-Ralph is telling the truth, because Tom is lying
Only one person is telling the truth in this scenario, so this is possible.
If Ralph is Guilty
-Peter is lying, because Tom is innocent
-Tom is telling the truth, because Ralph is guilty
-John is telling the truth, because he is innocent
-Ralph is lying, because Tom is telling the truth
Two people are telling the truth in this scenario, so Ralph cannot be guilty. John being guilty is the only scenario in which one person is telling the truth, therefore he must be guilty of killing Jeremy.
This solution does make the assumption that there's only one killer. If there's more than one killer then there are multiple possibilities, so we wouldn't have enough information to solve the puzzle.
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$\begingroup$ How does your answer add to the identical ones already given? You should always look at existing answers before providing one of your own, to ensure you are not just adding a duplicate. $\endgroup$– Rubio ♦Nov 27, 2017 at 19:45
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Who claims whom did it? A slight reformulation:
- Peter says: Tom
- Tom says: Ralph
- John says: Not John
- Ralph says: Not Ralph
What is true if each is lying?
- If Peter is lying: Tom did not kill Jeremy
- If Tom is lying: Ralph did not kill Jeremy
- If John is lying: John killed Jeremy
- If Ralph is lying: Ralph killed Jeremy
Look for pairs of speakers who cannot both be lying. Regardless of whether there is more than one killer, and regardless of whether any of the four actually did kill Jeremy:
Tom and Ralph cannot both be lying, since it cannot both be true that "Ralph did not kill Jeremy" and "Ralph killed Jeremy". Therefore the truth-teller is one of Tom or Ralph.
Also, if we assume that there is only one killer and it must be one of these four ("The Assumption"):
John and Ralph cannot both be lying, since that would mean both John and Ralph killed Jeremy. Therefore the truth-teller is one of John or Ralph.
In each of those pairs of people, at least one person must be telling the truth. But since there is only one truth-teller, the truth-teller must be the person in both pairs. Therefore the truth-teller is:
Ralph
Since only that person is telling the truth, we know that the killer is:
John, whose claim of innocence must be a lie.
But we can examine whether The Assumption was necessary.
Certainly at least one of the four must be guilty, or John and Ralph would both be telling the truth by claiming innocence. However, if more than one killer is allowed, then John and Ralph's claims of innocence could both be lies; this would imply they are both guilty, so Tom is correct that Ralph is guilty and must be the truth-teller. Working through the four statements, Tom tells the truth (so Ralph is guilty) while Peter lies (so Tom is innocent), John lies (so John is guilty) and Ralph lies (so Ralph is guilty). This clears Tom, but leaves Peter's guilt undetermined. Moreover if only one of John and Ralph's claims of innocence is correct, it must be Ralph's because we established earlier that the truth-teller is either Tom or Ralph. In this case Ralph tells the truth (so Ralph is innocent), Peter lies (so Tom is innocent), Tom lies (so Ralph is innocent) and John lies (so John is guilty). This is sufficient to establish that Ralph and Tom are innocent while John is guilty, but again not to establish whether or not Peter is guilty.
So if The Assumption is incorrect, and joint enterprise is allowed:
John is still certainly guilty and Tom is still certainly innocent. But Ralph and/or Peter may, or may not, have also taken part in the killing.
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Even without assumptions about multiple or a single murder, there is a single clear solution to this riddle:
John killed Jeremy
Peter and Tom just talk about Tom and Ralph being guilty - guilty can mean a lot of things, maybe they saw something and didn't help, or didn't come forward - or stole something from the body?
The only clear cut and important statements are those of John and Ralph. Johns statement is absolutely clear, if he is lying he killed Jeremy. And Ralphs statement about Tom leaves us only with two options without a contradiction: Either Ralph or Tom is telling the truth. - But which one doesn't matter, maybe Ralph is also guilty ? But the killer is John without a doubt!
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If John is telling the truth, then everyone else is lying, so Ralph is lying about Tom lying, but then Tom is telling the truth, which can not be. So John can't be telling the truth, so he did it.
