# A logic puzzle with some lateral thinking

Original puzzle below created by me. The writing is... to be honest, not that good, but it's a puzzle. Focus on the puzzle part.

Your name is John D. Tectif, and you're looking for 4 notorious criminals. All you know is that they go by Aaron, Bruce, Chris, and Dean. Rumor has it that they’ve teamed up for the first time, and this is likely true, given that a bank was robbed by exactly two people last week, even though they usually go solo. It couldn’t have been anyone else, since they’re the only criminals in the neighborhood. Luckily, you and your men have your suspects trapped in a bar. In addition, your old friend, a bartender, is there. He knows who everyone is, but he won’t provide much help due to his policy of customer confidentiality. However, you know that he is completely trustworthy and will never lie. He’s also told you beforehand that on the night of the crime, exactly two of the suspects were in the bar with him.

Your job is to question the other 4 men in the bar and figure out who’s who, and which of them pulled off the heist. In addition, the criminals happen to have some very convenient mental gimmicks, so you know that when questioned:

Aaron will tell a lie.

Bruce will tell the truth.

Chris will not lie.

Got it? Now, let’s begin.

You walk in, wary of any hidden traps. The bartender chuckles. “What a coincidence! All four of the criminals in town are right in front of me.” His eyes narrow. “You better not mess up my bar,” he warns. “I’m an innocent man.” What a shame. You were hoping to intimidate them with violence, but apparently that’s not allowed now.

“And who the heck are you?” asks one of the men.

“I’m John D. Tectif, and I’m going to solve this mystery.”

You bang your hands on the table. Intimidation might still be worth a try.

“Alright. Which one of you is Aaron?”

Both the first and third man from your left instantly decide to talk. “It’s not me!” they shout in unison. The second man snickers. “It’s actually him,” he says, gesturing to the first man. “I’m Bruce, by the way.” Alright then. That helps... maybe. The fourth man visibly squirms but stays silent. Not much help there. You decide to take a different route and bluff.

“I know that you were one of the thieves last week,” you say, pointing at the first man. The bartender raises his eyebrows. “Really? Because he was sitting right here, getting drunk at the time of the crime.”

...Come on, man. Can’t you help out a detective?

Suddenly, the fourth man yelps loudly. “It wasn’t me! I never robbed any banks!” The first two men turn on him immediately. “Liar!” “Stop lying!” Hmmm. Maybe you can get more information out of this fourth weak-looking guy. You ask him, “Who was the second guy here with during the crime?” you ask aggressively. The fourth man manages to get out “No one; he was alone-” before getting socked in the face. “Hey! We’ll rob you next! Do you want that?” says the first man. An empty threat. You stay silent, then repeat the question, “Who was the second guy here with during the crime?” this time addressed to the other three men. The first and third men simultaneously say “He was with me,” then glare at each other. The second man snickers again, more loudly this time.

“I was with him,” he says, pointing to the third man.

You’ve almost got enough information, so you decide to wrap it up quickly. “So these two pulled off the heist, right?” you say to the entire group, pointing to the second and third men. The second and fourth men quickly affirm “Yes,” which is followed by 1 growling, “Nope. They’re both lying.” Suddenly, the police chief busts his way in. “Hey! It's not safe in here! Tectif, get away while you handle them!” What a shame. Well, you’ve questioned them enough. Your job is done.

Who’s who and which two men pulled off the heist?

Hint 1:

There is a red herring. Make sure you read the given information carefully.

Hint 2:

This is lateral thinking for a reason. Are you making any implicit assumptions about who the people involved are? Note, however, that none of the information given is false (it's not that lateral)

• Would you like to use the tag [liars]? Jul 18, 2022 at 18:16

Question 1 - "Which one of you is Aaron?"

1. #1 is not Aaron.
2. #1 is Aaron.
3. #3 is not Aaron.
4. (stays silent)

Question 2 - "Who was #2 with during the crime?"

1. #2 was with #1 during the crime.
2. #2 was with #3 during the crime.
3. #2 was with #3 during the crime.
4. #2 was alone during the crime.

Question 3 - "So #2 and #3 pulled off the heist, right?"

1. No.
2. Yes.
3. (stays silent)
4. Yes.

Something is weird because

#2 agreed with #3 on Q2, and with #4 on Q3; but two of the criminals answer questions truthfully (if they answer at all), and the other two answer them falsely (if they answer at all).

In particular,

#2 agreed with #4 at one point (Q3) and disagreed with #4 at another (Q2)

which appears to show that

at least one of those two is not a criminal, and thus at least one of the criminals is not one of your four suspects. They could be a woman, or one of "your men" (but not the bartender, who truthfully declared himself innocent).

"Your job is to question the men and figure out which of them is guilty" is presumably a misdirect, in the vein of "Your job is to figure out which cup contains iocaine powder".

I suspect that the intended answer is:

#2 and #3 are guilty.

#4 lied (Q2) and told the truth (Q3), so a non-criminal.

#3 told the truth (Q2) and stayed silent (Q3), and is a criminal, so he's Chris.

#2 told the truth (Q2, Q3) and is a criminal, so he's Bruce.

#2 also told the truth in response to Q1, so #1 is Aaron, and Dean is someone else.

I also suspect that other answers are possible, but then the possibilities multiply in a hurry, and I didn't exhaustively analyze them and identify valid states of affairs versus self-contradictions.

Edit: Here's what I think I can come up with for other answers, though per the author, I'm still overlooking something. Each of the following scenarios is mutually exclusive with each of the others, and with the first one listed above.

Scenario:

#2 is guilty but #3 is innocent:

#1 lied (Q2) and told the truth (Q3), so a non-criminal.

#2 lied (Q2, Q3), so Aaron or Dean.

#3 lied (Q2), stayed silent (Q3, so not Aaron), and told the truth (Q1), so a non-criminal.

#4 stayed silent (Q1) and lied (Q2, Q3), so Dean or a non-criminal.

The other guilty one is either #4 (in which case he's Dean) or a non-suspect.

Scenario:

#2 is innocent but #3 is guilty.

#3 lied (Q2), stayed silent (Q3, so not Aaron), and told the truth (Q1) (contradiction, no criminal could do all three).

Scenario:

#2 and #3 are both innocent.

#2 lied (Q3).

#3 stayed silent (Q3, so not Aaron) and told the truth (Q1), so Bruce or Chris or a non-criminal.

#4 stayed silent (Q1) and lied (Q3), so Dean or a non-criminal.

The guilty ones are either #4 (in which case he's Dean) and a non-suspect, or two non-suspects.

• You're almost there. Reexamine the bartender's statements carefully. Jul 19, 2022 at 12:50
• Also, I believe the solution is unique, so only one answer is possible. Jul 19, 2022 at 14:17
• Are the following assumptions correct? (n) Gur onax jnf eboorq culfvpnyyl, abg ivn unpxvat be fbzrguvat. (o) Ba gur avtug bs gur pevzr, rknpgyl gjb bs gur fhfcrpgf jrer va gur one nyy avtug. (p) Guhf, gubfr gjb fhfcrpgf ner vaabprag. (q) #1 jnf bar bs gubfr gjb fhfcrpgf. Jul 19, 2022 at 15:25
• Lrf, gung'f pbeerpg. Jul 19, 2022 at 22:22
• I still don't get it, but I did edit my answer to flesh out the other scenarios as best I could manage. rot13(Vf Wbua uvzfrys bar bs gur pevzvanyf?) Though I don't get where that would matter (except to be amusing). Jul 20, 2022 at 1:49

The "rules" here seem bendy enough that I'm not sure this is correct and/or the only possible solution, but it seems like it could be the case that:

the four men, from first to fourth as referenced in the text, are Aaron, Bruce, Chris and Dean. Bruce and Chris pulled off the heist.

My reasoning is that:

the puzzle describes how the men will respond "when questioned," but doesn't indicate what they might otherwise do when not being directly questioned. Some of the statements are just outbursts in response to other suspects' statements, so we can't assume that they'd adhere to the same rules, e.g. I've concluded that the fourth person is Dean (and therefore will not answer truthfully when questioned), but some of his statements in the story are true, because they weren't made in response to a question from the detective.

• Actually, scratch that. The puzzle is correct in its current formulation. Your reasoning is incorrect because Jura lbh nfx, "gjb naq guerr chyyrq bss gur urvfg, evtug?" (juvpu vf n dhrfgvba) gur sbhegu crefba nafjref lrf. Haqre lbhe pbaqvgvbaf, gur sbhegu crefba jbhyq unir fnvq ab, be abguvat ng nyy (orpnhfr Qrna qbrf abg nafjre dhrfgvbaf gehgushyyl.) I added some clarification to that line, just in case. Jul 18, 2022 at 18:48
• Ah I see, rot13(V vavgvnyyl ernq gung yvar gb zrna gur dhrfgvba jnf orvat cbfrq gb 2 naq 3, abg gb gur jubyr tebhc.) Appreciate the clarification, back to the drawing board. Jul 18, 2022 at 18:59