Can you find out who is the killer behind this wedding ceremony case?

Your friend asked you to attend a wedding ceremony of his younger brother, Mike. The ceremony ran smoothly and lively. Mike and his wife, Cindy, looked blissful. However, it didn’t last long.

That afternoon, Mike was murdered. Someone killed him, Inspector said. You, as an investigator, now investigate the suspects in a closed room.

• Austin (Mike’s friend): "I didn’t murder Mike! Take a suspicion on Daniel, he is jealous for the wedding!"
• Daniel (Cindy’s friend): "Ah, yes, I AM jealous for the wedding though because I do fall in love with Cindy. But I didn’t kill him!"
• Cindy: "Enough! *sobbing* None of the four of us killed my husband."
• Bella (Cindy’s younger sister): "Yes. That’s true…"

Then your friend said that exactly three people in this room are lying for all of his/her statements. Who are the liars and who is the killer?

Clarification: your inspector is your only trustworthy person. He never lies to you, :)

• Is the remaining person telling the truth on all accounts? I think not. Also, this would probably be a more satisfying puzzle (or at least, a puzzle with more satisfying) if B and C weren’t saying the exact same thing.
– Bass
Commented Jan 15, 2018 at 6:50
• The grammar makes it unclear as to who said what with regards to the investigator. You make have luck having you observe what the investigator says because you are an investigator. Commented Jan 15, 2018 at 16:44

Solution 1:

Austin killed him. He is lying when he says he didn't kill him, and lying that Daniel is jealous. Daniel is also lying about being jealous, but telling the truth about not killing him. Bella and Cindy are both lying.
This answer assumes that 3 people lie in all their statements and the fourth tells the truth in at least one of their statements.

Solution 2:

Daniel killed him. He is lying when he says he didn't kill him, and lying about being jealous (and presumably killed him for some other reason). Austin is also lying about Daniel being jealous, but telling the truth about not killing him. Bella and Cindy are both lying.
Again this answer assumes that 3 people lie in all their statements and the fourth tells the truth in at least one of their statements.

Both the above are a bit unsatisfying because

There seems to be no reason for telling the lie that Daniel is jealous.

Solution 3:

All four are telling the truth. Your friend (Mike's older brother) is lying when he says exactly three people tell only lies. Your friend may be the killer.

• Completely agreed that your solution 3 is likely the intended answer. That the puzzle assigned that one statement to Mike's unnamed older brother instead of simply stating it as a fact pretty clearly spoils that this was the puzzle's intent. Commented Jan 15, 2018 at 23:37
• And yup, the third solution is indeed the answer! Congratulations! :D Commented Jan 16, 2018 at 0:10

Now, I'm completely new to puzzling.SE, so maybe I'm missing something, but the answer here seems remarkably clear to me:

No one killed Mike.

Mike's unnamed older brother says that three people present are lying. So the trick is to find the three people whose statements, when treated as false, result in there being no contradictions among all the statements we've received. So here we go!

Liar number one:

Inspector says that Mike was killed. But in truth, Mike is completely fine. Look; Mike just spilled a little wine on himself and went upstairs to change his shirt. He'll be right back down. You really need to calm down, dude; I think your job is starting to get to you.

Inspector is the first liar.

Liar number two:

Okay, I know what you're thinking.

You're thinking this answer is already completely invalid, because @athin told us in a clarification that Inspector isn't one of the liars. And you would be correct, except that @athin is also a liar.

As proof, I need only point out that @athin says that I am an investigator.

But in truth I am not an investigator; I am a chartered accountant. Therefore, @athin is liar number two, and the clarification claiming that Inspector isn't a liar proof-positive confirms that Inspector is, in fact, one of the other two liars.

That brings us to liar number three:

Okay, I know I said that I'm a chartered accountant, but.. well.. you caught me, that was a little bit of a fib. I am actually a professional orange-taster. I'm very sensitive about it and don't like to talk about it, but you and your accusatory stabby eyes pried it out of me.

I hope you're happy. Brute.

Anyhow, I guess if you're going to be pedantic about it, I'm not actually new to puzzling.SE; I've been here for a couple years, mostly lurking over in the lateral-thinking puzzles. I only ventured out because of the open bar at the wedding reception.

Oh, and while we're being completely honest with each other, I guess I should confess that Mike doesn't actually have an older brother; I just made him up and claimed he was my friend to get into the reception and the open bar. I'm kind of shocked that fooled any of you; I mean, I didn't even give him a name! I just kept referring to him as "Mike's older brother" and "my friend", and nobody asked any questions. I mean, what sort of rubes are you people?

So.. okay, I guess I'll cop to being liar number three.

Austin, Daniel, Cindy, and Bella all claimed not to have killed Mike. And as we've established that the Inspector was lying about Mike being dead, there is no contradiction here.

Additionally, Austin tells us that Daniel was jealous, and Daniel agrees that he was jealous, so there's no contradiction there, either.

Finally, Mike's older brother is also not one of the liars. That's in part because he doesn't exist (because I made him up), but also because his only statement was that three people were lying, which turned out to be entirely true.

QED.

Hope that clears things up!

• OMG, have a +1 from me XD, this is a great answer but it's soo weeirrd (a.k.a no, you can't make yourself a liar @Trevor Powell haha) Commented Jan 16, 2018 at 0:09
• @athin but Trevor Powell said you are a liar so you can make yourself a liar. cool. Commented Dec 29, 2020 at 20:29

My solution to this problem:

Cindy and Bella are necessarily false as one confirms the other, so they would both be completely true if one was, and there is only room for one person speaking the truth. So it is between Austin and Daniel who is lying and who speaks truth.. Daniel's statement that he was jealous for the wedding because he fell in love with Cindy adds an additional claim compared to Austin's assertion that Daniel was jealous for the wedding but without giving a reason why. So while Austin's more general statement cannot be false without Daniel's also being false, Daniel's can certainly be false on account of being jealous for a different reason than given, with Austin's still being true. That leaves the only arrangement in which one person speaks the truth in all their statements and three others lie in all of theirs one where Austin speaks the truth. All of Daniel's statements must then be false, including the assertion that he did not kill Mike - so Daniel is our murderer. As we do know that it must be true that Daniel was jealous for the wedding, but false that he was so because he fell in love with Cindy, it is actually a valid possibility for the motive that Daniel had fallen love with Mike..

Austin (Mike’s friend): "I didn’t murder Mike! Take a suspicion on Daniel, he is jealous for the wedding!"

Daniel (Cindy’s friend): "Ah, yes, I AM jealous for the wedding though because I do fall in love with Cindy. But I didn’t kill him!"

Cindy: "Enough! sobbing None of the four of us killed my husband."

Bella (Cindy’s younger sister): "Yes. That’s true…"

We can throw Austin and Daniel in the same boat - since ALL of the statements are either true or false per person, and they both claim Daniel is jealous.

I'm fascinated by Cindy's wording - "None of the four of us". I'm wondering if we should take that to mean not one was involved, or it wasn't just a single person involved. I'm guessing the ambiguity here is what allows this to have the answer it does.

Bella simply claims Cindy's statement is true, but if we read Cindy's statement as ambiguous then I'm going to suggest:

Bella, Daniel, and Austin are, together, the murderers, and Cindy the only truthful person

If so, then:

* Austin: I killed him, Daniel isn't jealous
* Daniel: I'm not jealous, I killed him
* Cindy: More than a single individual was involved (truth - matches her statement if ambiguity is understood one way)
* Bella: Someone in this group killed him (again, the opposite of something Cindy's statement could be taken to mean)

• I like the insight here that Austin and Daniel have made the same statement (re: Daniel's jealousy), in exactly the same way that Ciny and Bella are making the same statement. This means that it's impossible for there to be an odd number of liars; because of the equivalence of the statements in the puzzle, liars and truth-tellers must come in pairs. Commented Jan 15, 2018 at 23:27

My guess is

Bella kille Mike because she was in love with him. Clearly, she did not want to kill her sister, and moreover there is someone to blame.

remember that

Daniel is in love with the bride. This way, Bella will never have to see the man she loves and her sister being together, and the whole crime can be pinned on Daniel.

• It was only ever a matter of time before people started shipping the characters in puzzling.SE submissions. :) Commented Jan 15, 2018 at 9:09
• "she did not want to kill her sister" but killing the man she loves is not a problem for her. Waw Commented Jan 15, 2018 at 13:26
• Of course not. Mike is completely wrong for Cindy, and Bella is just saving her from a divorce. This combined with having to see her ex, Mike, at family events (once he realizes Bella is The One,) would be a much bigger pain for her in the end. Commented Jan 15, 2018 at 15:26

The killer is probably

Austin

The reasoning being that

All statements 3 people make must be false, but the other's statements may also be false, so long as at least 1 is true.

Daniel has picked a really lousy time to be sarcastic (people have been shipping him with Cindy since they were 6, even though he has been out of the closet for more than half of that time.) He didn't kill Mike though. So he isn't one of the horrible liars.

Cindy and Bella are wrong, and Austin is lying about not being the killer and trying to shift the blame.