Is this logic puzzle legit?

The Game Room
1

I was just trying to solve a daily logic puzzle 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?

2

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.

3

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”.

4

I guess it could have been Alex+Brook+Charlie+Dale. Then, the four “it was” statements are true, and also “it wasn’t Emery”.

5

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
6

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
7

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…

8

Plus an infinite number of additional ones with Frank, George, Herbert, etc.

9

That path leads to madness.

10

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.

11

The police managed to get “a” confession. That’s all the info needed to make the obvious assumption necessary.

12

Not necessarily (if we want to be really picky).

“I confess that Munch and I did it.”

13

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.

14

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.

15

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.

16

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.

17

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.

18

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.

19

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.

20

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.