# Is this logic puzzle legit? **URL:** \ **Category:** The Game Room\ **Created:** [September 22, 2023, 10:21pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561 "2023-09-22T22:21:39Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 22, 2023, 10:21pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/1 "2023-09-22T22:21:39Z")
I was just trying to solve a [daily logic puzzle](https://www.brainbashers.com/puzzle/zwtl) by Kevin Stone. Here’s the puzzle: > After a local bungled heist, five suspects were being interviewed by the police. > > Eventually, the police managed to get a confession. > > Below is a summary of their statements and it turns out that exactly **5** of these statements were true. > > Would you make a good detective, try and work out who committed the crime? > Alex said: > It wasn’t Brook > It was Charlie > > Brook said: > It wasn’t Alex > It was Dale > > Charlie said: > It wasn’t Dale > It wasn’t Brook > > Dale said: > It wasn’t Emery > It was Alex > > Emery said: > It wasn’t Charlie > It was Dale I was unable to solve this puzzle. When I gave up and read the answer, I found that an assumption was necessary to solve the puzzle and I feel that assumption was not apparent from the text of the puzzle. Only one of the five suspects is guilty. I feel there’s nothing in the text of the puzzle to indicate that there’s only one guilty person. Do other people feel that this assumption is not there? Or do you feel it is there and I was wrong not to see it? ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [September 22, 2023, 10:28pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/2 "2023-09-22T22:28:25Z")
While not 100% obvious, I think from the way the question and the responses were phrased, plus the way these logic puzzles usually work, that it’s a fairly safe assumption. If the assumption were not true, it makes some aspects of how things were worded seem really odd. Since you spoilered the assumption, I don’t want to go into more detail. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 22, 2023, 10:38pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/3 "2023-09-22T22:38:55Z")
The phrasing “it was” and “it wasn’t” seems to hint at it being a single person. I haven’t worked through all the possibilities, but it may be that there’s no multi-person solution anyway. The puzzle also doesn’t specify that the criminal is one of the suspects. Though if that’s the case, then there are 6 true statements, so it can be inferred. It was Emery. All but one of the “it wasn’t” statements are true, and none of the “it was”. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 22, 2023, 10:41pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/4 "2023-09-22T22:41:04Z")
I guess it could have been Alex+Brook+Charlie+Dale. Then, the four “it was” statements are true, and also “it wasn’t Emery”. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [September 22, 2023, 10:46pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/5 "2023-09-22T22:46:21Z")
I solved it by making that assumption. You’re right that the exact language doesn’t explicitly state that, but I felt it was an obvious assumption for a couple reasons: - the suspects say “it was \_\_\_”, not “one of the people was \_\_\_” - it is impossible to solve if you don’t make that assumption ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [September 22, 2023, 10:51pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/6 "2023-09-22T22:51:43Z")
> [@Dr.Strangelove](#): > > I haven’t worked through all the possibilities, but it may be that there’s no multi-person solution anyway. I of course had to make a spreadsheet. There are actually several: - Alex + Emery - Brook + Dale - Charlie + Emery - Alex + Brook + Dale - Alex + Charlie + Emery - Brook + Charlie + Emery - Alex + Brook + Charlie + Dale ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [September 22, 2023, 10:53pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/7 "2023-09-22T22:53:14Z")
Without reading any of the spoilers, my answer is Charlie. ETA: OK, I did make that assumption. But also I solved it wrong. Let me look at the little grid I made again… ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 22, 2023, 10:55pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/8 "2023-09-22T22:55:35Z")
> [@TroutMan](#): > > I of course had to make a spreadsheet. There are actually several: Plus an infinite number of additional ones with Frank, George, Herbert, etc. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [September 22, 2023, 10:57pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/9 "2023-09-22T22:57:56Z")
That path leads to madness. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [September 22, 2023, 10:58pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/10 "2023-09-22T22:58:19Z")
> [@Dr.Strangelove](#): > > The phrasing “it was” and “it wasn’t” seems to hint at it being a single person. This, plus it being “ **a** confession”. I suspect that you can solve the puzzle simply by iterating through the suspects and assuming that one to be the guilty one. If exactly 5 of the statements are true under that scenario then that’s the correct answer. ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [September 22, 2023, 10:59pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/11 "2023-09-22T22:59:05Z")
The police managed to get “a” confession. That’s all the info needed to make the obvious assumption necessary. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [September 22, 2023, 11:00pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/12 "2023-09-22T23:00:05Z")
Not necessarily (if we want to be really picky). “I confess that Munch and I did it.” ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [September 22, 2023, 11:01pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/13 "2023-09-22T23:01:26Z")
As a side note, I’d generally take the full contents of what a person says as their “statement”, not each discrete sentence. But that makes the puzzle impossible so it’s clearly not the correct read. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [September 22, 2023, 11:03pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/14 "2023-09-22T23:03:31Z")
> [@Sage\_Rat](#): > > I suspect that you can solve the puzzle simply by iterating through the suspects and assuming that one to be the guilty one That’s what I ended up doing to the side of my grid to get to the right answer of Emery. I’m sure there is a cleverer way that I’m missing. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 22, 2023, 11:17pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/15 "2023-09-22T23:17:11Z")
> [@Folly](#): > > I’m sure there is a cleverer way that I’m missing. Well, only slightly easier. All the suspects except Brook lead to 5 correct “it wasn’t” statements. And it wasn’t Brook since no one said “it was Brook”, which would be needed to get the 5 total true statements. Since it wasn’t Brook, it must be someone without an “it was” statement, and that leaves only Emery. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 23, 2023, 12:48am UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/16 "2023-09-23T00:48:06Z")
> [@Dr.Strangelove](#): > > I haven’t worked through all the possibilities, but it may be that there’s no multi-person solution anyway. No, I worked on it and I came up with several multi-purpose solutions based on there being five false statements. Consider these two pairs of statements: _Alex said: It was Charlie_ _Emery said: It wasn’t Charlie_ _Dale said: It was Alex_ _Brook said: It wasn’t Alex_ In each pair, one statement must be true and one statement must be false. So this means we have exactly two false statements and two true statements in the group. So we know that three of the other six statements must be false. _Brook said: It was Dale_ _Emery said: It was Dale_ _Charlie said: It wasn’t Dale_ _Alex said: It wasn’t Brook_ _Charlie said: It wasn’t Brook_ _Dale said: It wasn’t Emery_ Now test two assumptions. First assume Dale is guilty. If so, then _Brook said: It was Dale_ and _Emery said: It was Dale_ are true and _Charlie said: It wasn’t Dale_ is false. Added to the statements from above, this gives us four true statements and three false statements. So two of the remaining three statements must be false. Obviously _Alex said: It wasn’t Brook_ and _Charlie said: It wasn’t Brook_ must either both be false or both be true. As we know there are two false statements, they must be false which means Brook is guilty. And having found all five false statements, we know the remaining statements _Dale said: It wasn’t Emery_ must be true is Emery is innocent. Now assume Dale is innocent. If so, then _Brook said: It was Dale_ and _Emery said: It was Dale_ are false and _Charlie said: It wasn’t Dale_ is true. Again adding in the totals from above, this time we get four false statements and three true statements. So _Alex said: It wasn’t Brook_ and _Charlie said: It wasn’t Brook_ must both be true and _Dale said: It wasn’t Emery_ must be false in order to get the correct total of five false statements. So based on this, we know that if Dale is guilty, it means Brook is also guilty and Emery is innocent. And if Dale is innocent, it means Brook is also innocent and Emery is guilty. And that’s where I got stuck. I couldn’t see a way to deduce which of those conclusions was correct, much less untangle Alex’s and Charlie’s guilt or innocence. I had eight possible answers, all of which were equally possible, assuming multiple guilt was allowed. Dale and Brook innocent, Emery guilty. Alex and Charlie innocent. Dale and Brook innocent, Emery guilty. Alex innocent and Charlie guilty. Dale and Brook innocent, Emery guilty. Alex guilty and Charlie innocent. Dale and Brook innocent, Emery guilty. Alex and Charlie guilty. Dale and Brook guilty, Emery innocent. Alex and Charlie innocent. Dale and Brook guilty, Emery innocent. Alex innocent and Charlie guilty. Dale and Brook guilty, Emery innocent. Alex guilty and Charlie innocent. Dale and Brook guilty, Emery innocent. Alex and Charlie guilty. Any of these scenarios produces five false statements. But if I had understood the implied assumption, I would have had the answer. If I had known there was only one guilty person, I would have known Dale and Brook couldn’t both be both guilty. And if Dale and Brook are innocent, then Emery is guilty. And if Emery is the sole guilty one, then Alex and Charles are innocent. Or just looking at the set of eight possible answers, I would have seen that only one had a single guilty person. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 23, 2023, 1:01am UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/17 "2023-09-23T01:01:03Z")
On a broader note, this is an issue I’ve encountered in these types of puzzles before. The authors want you to assume the standard usage of the words in the text and will tell you your answer is wrong if it’s based on some other usage of any words. Unless they’ve developed a trick question which is based on some non-standard usage of some words in the text, in which case they’ll tell you you got the wrong answer because you only used the standard usage and didn’t consider the other possibilities. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 23, 2023, 1:05am UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/18 "2023-09-23T01:05:58Z")
All I can say is that the wording seemed fairly unambiguous to me. If there were multiple criminals, they’d have phrased it in some other way, as **TroutMan** suggested. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 23, 2023, 1:29am UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/19 "2023-09-23T01:29:13Z")
Perhaps it’s just from watching movies but when I see the word “heist” used, my default assumption is that it’s a crime carried out by a group of criminals, usually of a casino, museum, or jewelry exchange. My cites are Heist, Rififi, Topkapi, Thief, Sneakers, Kelly’s Heroes, Logan Lucky, Set It Off, Tower Heist, The Score, The Bank Job, The Great Train Robbery, The League of Gentlemen, The Thomas Crown Affair (1968 and 1999), The Italian Job (1969 and 2003), Point Break (1991 and 2015), Ocean’s Eleven (1960 and 2001), Ocean’s Twelve, Ocean’s Thirteen, and Ocean’s Eight. You don’t just go out and do a heist all by yourself; you need to get a crew together. So I figure Alex, Brook, Charlie, and Dale were all in on it. Part of their plan was setting Emery up as the fall guy. ---
**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\ **Post date:** [October 6, 2023, 6:31pm UTC](https://boards.straightdope.com/t/is-this-logic-puzzle-legit/990561/20 "2023-10-06T18:31:24Z")
> [@](#): > > > After a local bungled heist, five suspects were being interviewed by the police. > > > Eventually, the police managed to get a confession. > > > Below is a summary of their statements and it turns out that exactly **5** of these statements were true. > > > > Would you make a good detective, try and work out who committed the crime? > > Alex said: > > It wasn’t Brook > > It was Charlie > > > > Brook said: > > It wasn’t Alex > > It was Dale > > > > Charlie said: > > It wasn’t Dale > > It wasn’t Brook > > > > Dale said: > > It wasn’t Emery > > It was Alex > > > > Emery said: > > It wasn’t Charlie > > It was Dale I solved it by assuming that each suspect told one true and one false statement. Except for two of them; one of whom made two true statements, with the other one making two false statements. I also assumed that every WAS statement was a lie, and that (with the exception of one) every WASN’T statement was the truth. This is how I assessed them: Alex said: > It wasn’t Brook. **TRUE** > It was Charlie **FALSE** > > Brook said: > It wasn’t Alex. **TRUE** > It was Dale. **FALSE** > > Charlie said: > It wasn’t Dale. **TRUE** > It wasn’t Brook. **TRUE** > > Dale said: > It wasn’t Emery **FALSE** > It was Alex. **FALSE** > > Emery said: > It wasn’t Charlie **TRUE** > It was Dale. **FALSE** Since both of Charlie’s assertions were of someone it _wasn’t_, I assumed that he was the double truth teller. I just sort of arbitrarily picked Dale as the double liar, so it was Emery. This pretty much amounted to a lucky brute force solution, because although I can show that it works, I can’t systematically prove that no other solution does. I just went on faith that the writer had successfully constructed a puzzle with a unique solution.