On Friday I posted this puzzle….

There are four suspects, and one of them has committed a murder.  They make the following statements, but only one of them is telling the truth.  Who committed the murder?

Jon: James did it.
James: Bob did it.
Sid: I didn’t do it.
Bob: James is lying.

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

If Sid is innocent, then his statement is true and so the other three suspects are lying. But that means that Bob is also telling the truth, a contradiction. So Sid can’t be innocent and so he must be murderer.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. Navneeth says:

Eddie is lying.

2. Anonymous says:

Yes, why not?
Out took me a while to work out the solution but the answer is absolute.

3. Anonymous says:

I was initially convinced by Richard’s solution, Eddie, but now I have seen your clear, thorough, well-structured and insightful refutation I realise that Richard got it wrong.

4. Richard’s answer is, of course, correct given the premise. Just plug in all four names and you see that Sid’s is the only one that fits with three lies.

However, the premise is rather strange. The murder is identified as the person where the greatest number of people lie, rather the opposite of what you might expect in real life where James is would surely be the main suspect as he would be the only one telling a lie (and has an obvious motive to do so) whilst the other three response are all consistent with him being the murderer.

1. Neil says:

Or: One of James and Bob is telling the truth, the other is lying. Therefore Jon and Sid are both lying and Syd is guilty.

1. Navneeth says:

If James is telling the truth, it would imply that Sid is also telling the truth.

And Bob telling the truth is the solution provided by Dr. Wiseman.

2. Turd says:

Neil please read the question all over again.

2. Baker's Dozen says:

How do we know one is telling the truth? Phone hacking?

3. Anne Elk says:

It’s taken me ten minutes to understand the *solution*. There’s no chance I would have got this. I can see that it creates a kind of loop.

1. ChrisR says:

The best (?) approach to this (which might be a sledge-hammer) would be to look at each person and think that if they were the murderer are the comments true or false?
So if Jon is the murderer, his and James comments are false, but Sid’s and Bob’s are both true. So as there are two true comments Jon is not the murderer.
If James is the murderer, then his is the only false comment and the other three are true – so he is not the right answer.
If Sid is the murderer, then there is only one true statement (Bob’s). Puzzle solved.
But to check the veracity and completeness of the puzzle, we also consider if Bob is the murderer: in this case both James’ and Sid’s comments are true.

I found the most confusion between James and Bob – if James is lying then Bob is telling the truth and vice versa.

But we’re still waiting for Skatz to explain their short-cut…

4. pete says:

Just take the Judge Death approach to jurisprudence.

5. Simple. Bob or James are telling the truth as their statements are opposite. This means everyone else is lying which means Sid, who says he didn’t do it, did it.

6. mittfh says:

Jon claims James is guilty, so implies that Jon, Sid and Bob are innocent.
James claims Bob is guilty, so implies that Jon, James and Sid are innocent.
Sid claims he’s innocent, so implies that Jon, James and Bob are suspects.
Bob effectively claims he’s innocent, so implies that Jon, James and Sid are suspects.

If either Jon or James is telling the truth, then Sid must also be telling the truth – but presumably all four have been subjected to polygraph tests, so we know only one’s telling the truth and the other three are lying. Therefore both scenarios can be discounted as a possibility.

If Sid’s telling the truth, then from Jon and James’ answers, we know the guilty party can’t be James or Bob. But Bob’s answer indicates that James is telling the truth, which means that either James or Bob are also telling the truth – so again we’re left with two suspects telling the truth, so this scenario can also be discounted as a possibility.

If Bob’s telling the truth, then by reversing the others’ answers, James is innocent, Bob’s innocent and Sid’s guilty – this scenario is the only one in which it’s possible for only one of the suspects to be telling the truth.

Having said that, technically Jon and James could also potentially be arrested for a different offence: perverting the course of justice.

7. Lazy T says:

Yes, but society is to blame…

8. Here’s the way I approach problems of this kind. It’s not as efficient as Richards solution in this case, but it works:

Jon guilty James guilty Sid guilty Bob guilty
Jon: James did it. F T F F
James: Bob did it. F F F T
Sid: I didn’t do it. T T F T
Bob: James is lying. T F T T

The table shows which statements are true and false depending on who’s guilty. The only column that shows exactly one person telling the truth is “Sid guilty”.

1. Let’s try that again (without the spaces gobbled up)…

Here’s the way I approach problems of this kind It’s not as efficient as Richard’s solution in this case, but it works:

………………………………………Jon.guilty…..James.guilty…..Sid.guilty…..Bob.guilty
Jon:.James.did.it…………………..F………………….T…………………..F………………..F
James:.Bob.did.it………………….F………………….F…………………..F………………..T
Sid:.I.didn’t.do.it………………….T………………….T…………………..F………………..T
Bob:.James.is.lying………………T………………….F…………………..T………………..T

The table shows which statements are true and false depending on who’s guilty. The only column that shows exactly one person telling the truth is “Sid.guilty”.

2. OK, now I’m getting anal about getting the spacing right… One more try:

………………………………………Jon.guilty…..James.guilty…..Sid.guilty…..Bob.guilty
Jon: James did it…………………………F……………T………………F…………….F
James: Bob did it………………………..F…………….F………………F…………….T
Sid: I didn’t.do it………………………..T……………T………………F…………….T
Bob: James is lying………………………T……………F………………T…………….T

3. One more try (getting anal now):
………………………………………Jon.guilty…..James.guilty…..Sid.guilty…..Bob.guilty
Jon: James did it…………………………F……………T………………F…………….F
James: Bob did it………………………..F…………….F………………F…………….T
Sid: I didn’t.do it………………………..T……………T………………F…………….T
Bob: James is lying………………………T……………F………………T…………….T

4. ChrisR says:

except James guilty has James lying, and Bob telling the truth
and Bob guilty has James telling the truth and Bob lying
🙂

9. Peter Farrant says:

Awesome! My first Friday puzzle and I got I correct.

1. Right Chris, it should be
………………………………………Jon.guilty…..James.guilty…..Sid.guilty…..Bob.guilty
Jon: James did it…………………………F……………T………………F…………….F
James: Bob did it………………………..F…………….F………………F…………….T
Sid: I didn’t.do it………………………..T……………T………………F…………….T
Bob: James is lying………………………T……………T………………T…………….F

I should have paid more attention to content than format. 🙂

10. The key to getting straight to the answer without having to tabulate all the possibilities is to look for statements that are about the truth of other statements.

Here there’s only one such statment: Bob states that James is lying. So either Bob are James are the truth-teller. (If Bob’s statement is true then obviously he’s the truth-teller; if Bob’s statement is a lie then it’s false that James is lying, so James must be the truth-teller.)

Either way, Jon and Sid must both be lying. (Because there’s only one truth-teller, and we know it must be either Bob or James.)

So Sid is lying when he states he didn’t do it. Which means he did it.

Note that it isn’t necessary to consider what either Jon or James said.

I’m not Skatz, but I presume this is what he/she meant by the claim on Friday that you can get the answer from what only two of the suspects are saying.

1. ChrisR says:

Thanks – that’s very helpful and insightful

2. Bah in “either Bob are James are the truth-teller” the first “are” should be “or” and the second “are” should be “is”. Sorry for not proofreading more carefully.

3. Slow Learner says:

Smylers
Thank you for this, which gave me a genuine insight, which I had not had before.
However, even with this, it is still necessary to look at at least three statements to get to the solution – Bob’s and James’ followed by Sid’s.
Of course, if you look at Jon’s after the first two, you then need to look at Sid’s statement too [Jon’s, James’ and Bob’s statement on their own are consistent with Bob having done it and there being only one truth teller], so Skatz’ contention that you only need to look at two statements appears to be incorrect.

4. Slow Learner: No, it isn’t necessary to look at James’s statement at all to solve the puzzle.

Bob’s statement on its own is sufficient to determine that one of Bob or James must be the truth-teller, and you can then go on to Sid’s statement without looking at James’s.

(You do need to look at James’s statement in order to work out which of Bob and James is the truth-teller. But identifying the murderer doesn’t actually require working out who the truth-teller is.)

5. ChrisR says:

Of course, you do need to look at all (or most of) the comments to work out which are the two that you need. And you also perhaps ought to check for consistency – for example if Jon had said ‘Sid did it’ then the puzzle would be flawed and there wouldn’t have been a solution.
But we of course trust Richard to not get it wrong.

11. ivan says:

Richard’s argument is in fact a sufficient complete demonstration of the solution: he shows that it is a solution and that it is the only possible solution. However it depends upon spotting the short cut. Given the premise that only one person is telling the truth, then Sid’s statement “I didn’t do it” is very helpful, either he did do it, or everyone else is lying. We can quickly discern which. If you don’t spot the short cut, you’ll just have to try the four possibilities.

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