# A murder mystery I’ll host at a bar

I’m hosting game night at my regular bar, and I’m gong to stage a murder mystery. Each of the suspect will make 4 statements, one of which is known to be a lie.

I tried to construct it as soundly as I could, using a grid to check each person’s lies and truths. I based it roughly on this other puzzle I found here:

Who is the thief? An elementary school teacher had her purse stolen

I just want to check that it’s interesting enough and that the logic checks out.

Kevin (the bar owner) is murdered, and there are four suspects. A partially-burned note is found in the garbage (I know, it’s just a game) that says “I know you paid to have Kevin killed, pay me or suffer the consequences”. The game is to identify the killer, the person who hired the murderer, and the blackmailer (revealing the last person as totally innocent).

Here are the four statements of all the suspects, can you solve it? I’d appreciate it if you could point out any logical errors and ways to improve or fix the puzzle, thanks.

1. Matt: I did not kill Kevin

2. Amy: I did not kill Kevin

3. Graham: I did not kill Kevin

4. Kristen: I did not kill Kevin

5. Matt: I’ve known Amy all my life, she’ll vouch for me

6. Amy: I don’t know what Matt’s talking about, I only met him a few months ago

7. Graham: Amy doesn’t know who did it

8. Kristen: Matt knows who did it

9. Matt: I’m totally innocent in all matters regarding this crime

10. Amy: Kristen knows I didn’t kill Kevin

11. Graham: Kristen knows who did it

12. Kristen: Matt killed Kevin

13. Matt: Graham killed Kevin

14. Amy: Kristen killed Kevin

15. Graham: Kristen is not the blackmailer

16. Kristen: Amy is the blackmailer

• Checking whether I've understood the "rules" correctly: some people don't know everything; if someone says something they're not in a position to know is true or false, is it (1) always a lie, (2) never a lie, or (3) a lie if and only if it's actually false? And are we to understand that everyone lies exactly once? – Gareth McCaughan Nov 25 '17 at 11:18
• Everyone lies once, and nobody makes a statement if they don’t know something - the statement may be a lie, but if it is, they know the truth of it and know they’re lying. – Tony De Jesus Nov 25 '17 at 11:26

Taking the rules to mean that each person makes exactly one false statement, I think this puzzle currently has a unique solution, as intended:

Amy blackmailed Kristen for paying Graham to kill Kevin; Matt is innocent.

Here's how the reasoning goes:

Matt says multiple things implying he isn't the killer, but only lies once, so Matt is not the killer. Ditto for Kristen. Ditto for Amy. Therefore Graham is the killer.

Now Graham's

second statement is known to be false, so the others are true. So Amy doesn't know who did it (so she is neither the killer nor the hirer, but she could be the blackmailer); Kristen is not the blackmailer (and also not the killer, so she is either innocent or the hirer); and Kristen knows who did it. (Does this mean she must have paid for the hit? No, though it will turn out that she did.)

Now Amy

says Kristen is the killer, which is false; her other statements are that Amy isn't the killer (true), that she only met Matt recently (which we therefore now know is true), and that Kristen knows Amy isn't the killer (fair enough, but this doesn't tell us anything new).

Kristen

says Matt is the killer, which is false, so her other statements are true: Amy is the blackmailer (consistent with what we know so far), Kristen isn't the killer (already known), and Matt knows who did it (which we now know is true). Note that we now know that both Kristen and Matt know who did it; one of them is innocent despite this, and the other one paid for the killing.

So now we have established that

Graham is the killer and Amy the blackmailer.

What does Matt have to say?

He says Amy will vouch for him, having known him for ages; both halves of this are false (see above). So the other things he says are true: Graham is the killer (we already knew this), Matt isn't the killer (we already knew this), and Matt is wholly innocent (this is new, and tells us that Kristen is the hirer).

This establishes the identities of the criminals as given at the top of this answer. My only qualms are

that Matt has lied about the crime (but that's OK since he doesn't do so until after declaring his total innocence) and that Matt knows who committed it, which suggests some degree of complicity since evidently the crime is still being investigated...

• Exactly, thanks! I was hoping to add more facts to add some motive as to why did what they did, (Graham owes Kristen money, who will forgive the debt if he kills Kevin, who was her lover but broke up with her.) but I’ll make a “confessional roundl where the players will read their confessions explaining their motives. Thanks for your help! – Tony De Jesus Nov 25 '17 at 11:34
• Not sure I agree with the logic as presented: Kristen knowing who did it does not make her necessarily guilty of anything (Matt knows it too). We need to determine that Matt's declaration of innocence is true before we determine Kristen's role by elimination. – ffao Nov 25 '17 at 13:14
• Perhaps one of us is misunderstanding the other somehow; my solution doesn't use that information, though I do comment that it's interesting that it's there. – Gareth McCaughan Nov 25 '17 at 13:33
• I immediately followed the statement of Kristen knowing who did it with Kristen saying Matt did it to send the players down the wrong alley. They may think Matt did it, but then they have to determine whether one or both of the prior statements was a lie once the grid doesn’t check out; also introducing the idea that Kristen is trying to frame the innocent guy. – Tony De Jesus Nov 25 '17 at 17:07
• I'm referring to this sentence, especially the last part in brackets: "Kristen is not the blackmailer (and also not the killer, so she is either innocent or the hirer); and Kristen knows who did it (so in fact she must have paid for the hit)." – ffao Nov 25 '17 at 20:11