Last week Richard Saunders was in Edinburgh and kindly interviewed me for his weekly podcast The Skeptic Zone – you can listen to it here.

So, to the puzzle……

The people who live on the next street are strange.  Those who live at odd numbered houses always lie, and those who live at even numbered houses always tell the truth.

The other day I met a group of three people from the next street and asked them whether they were from odd or even numbered houses. The first one murmured something that was too soft to hear. The second replied, “He said he was from an odd numbered house.” The third then said to the second, “You are a liar!”

Did the third person live at an odd or even numbered house?

If you haven’t tried to solve the puzzle, have a go now.  For everyone else, the answer is after the break.

If the first person was from an even numbered house, they would say so. If the person was from an odd numbered house, they would say that they were from an even numbered house.  Therefore, the second person had to be lying. The third person truthfully identified the liar and was therefore telling the truth, so they must live in an even numbered building.

Did you solve it?

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

The third is leaving at a even numbered house.
The statement “He said he was from an odd numbered house.” is a lie. The first person cannot say “i am from a odd number house” because in the given conditions it is a impossible statement.

*is living ( i hate you cannot edit your posts )

3. Letitia says:

Yes.

4. Hugh Janus says:

Do the houses have flagpoles?

Yes. And every other one flies the flag of Crete.

5. Yes, laughably easy and free from ambiguities.

Good puzzle Richard.

1. Anonymous says:

If it was laughably easy, why do you consider it a good puzzle?

2. I found it enjoyable and a nice way to exercise the mind briefly on Friday morning. Is that okay with you Mrs Anonymous?

3. Dave says:

That’s hardly the same thing as being “laughably easy”. I think you were just trying to show off.

4. Mrs Dave, Do you? Is it not written “People who assume the worst in others are probably up to no good themselves.”

5. Berber Anna says:

Why would you call someone named Dave ‘mrs’? That’s a traditionally male name. If it’s an attempt at an insult, why do you feel that being compared to a married woman is insulting?

I agree with you that the puzzle was nice and easy, but your use of ‘mrs’ baffles me.

6. Not a big Papa Lazarou fan then.

“If it’s an attempt at an insult”

Is it not written “People who assume the worst in others are probably up to no good themselves.”

7. Berber Anna says:

Ah. Just looked that up on Wikipedia. I do watch some British shows, but I’ve never seen League of Gentlemen, no.

I’m not assuming the worst, I was asking. Assuming and asking are usually mutually exclusive. But I have noticed a pattern of people using terms that don’t apply to a person (gay for straight people, retarded for people who don’t suffer from mental retardation, little girl for grown men) in an attempt to insult that person. Mrs obviously is a term that does not apply to males, so I thought that your use of it might conform to this pattern.

6. John says:

The statement was that the first person murmured something too quietly to hear, therefore the second person was lying when he claimed that the first person said something definite.

We have, again, an answer that does not fit in with the problem as stated. It would have been a nice problem if it was “too quiet for me to hear”, but “too quiet to hear” means that no-one could hear it.

1. Chris says:

whether the 2d person actually heard the statement does not affect the solution. the puzzle is designed so that no person could ever say they lived in an odd-numbered house.

2. Richard says:

Doesn’t matter does it? Whichever, the second person was still lying and the third was still telling the truth. So the answer *does* fit with the problem as stated.

7. Beaky says:

Agree with Damocles – easy AND free from ambiguities.
Anyone can nitpick this puzzle, but let’s keep it simple:

1. Puzzle states that all three people are from the “next street”.
(logical assumption is that they all know about proclivities
of odd- and even-numbered residents.)
2. When #1 says something in response to question “do you live
in odd or even-numbered house”, next logical assumption is
the weather or saying “Huh?”. But it doesn’t matter what #1
said, or didn’t say.
3. Sound diminishes in loudness with distance. Just because
the poser of the puzzle could not hear #1’s response doesn’t
mean person # 2 couldn’t hear it. And as already pointed out
it’s irrelevant. Even if #2 was deaf, his statement that
#1 said “odd” is a lie. OK?
4. So, of course, #3 is telling truth, and lives in even-numbered house.

5. The flagpole DOES have a flag, and #4 IS wearing a blue hat.
(Those are so obvious I won’t bore you with the derivations.)

1. Karl Withakay says:

So Beaky, without one of the following assumptions about #3, how does 3 know 2 is lying?

A #3 Heard #1′s answer (or does not erroneously believe they understood #1’s answer to be odd)*
B #3 Knows where #1 lives and assumes #1 did not lie when mumbling
C #3 Knows that all odds lie & all evens tell the truth AND understands logic well enough to reason out the truthfulness of #2′s statement.

* &/or knows #2 did not hear #1 such that #2 is lying when claiming to know what #1 said.

It seems that C is the most likely assumption intended in the puzzle.

Also If #2 was unaware of the rules (regarding who lies and tells the truth) and mis-heard #1 so that #2 believed they heard #1 say #1 lived in odd numbered house, they would believe their statement was true

2. Anonymous says:

Whether #3 know’s if #2’s statement was a lie is irrelevant. #3 said “You are a liar!”, not “That was a lie!”
The only relevance of #2’s specific statement is that we can determine if he’s lying or not, and thus whether #3’s claim is true.

8. Mervulon says:

Nice, straight forward puzzle. But I’m from an odd numbered house.

9. Anonymous says:

A: Yes. He lives at an odd-numbered house or an even-numbered house. There are no other options.

10. dharmaruci says:

The first person lived at no 14, but it is labelled as 13A by the superstitious.

So person Uno said “I live at an odd numbered house” and was telling the truth….The number is indeed odd in the sense of particular.

That makes the 2nd person a truthist and the third a liar.

11. Danon says:

First persons response would have been “I own and live in both an even and odd numbered house an equal amount of time.”

Thus the second person would be telling the truth technically, but still it would be the truth.

The third persons response could then be either true or false, because if he said that the second person was lying in regards to not telling the whole truth, then he would be telling a version of the truth.

But if the third person was saying that the second was lying because the first person never said “I live in an off numbered house”, then the third would be lying flat out.

So if the first persons statement was he was a multiple home owner and lived in both his houses equal time then the third person could be either telling the truth or telling a lie.

1. “Those who live at odd numbered houses always lie, and those who live at even numbered houses always tell the truth.”

This statement of facts means that person #1 cannot have both odd and even numbers, as nobody can always tell the truth and also always tell lies.

Your alternative answer, therefore, is based on ignoring the given information. For you to be correct, it would have to say, for example, ‘when living in an odd-numbered house, only lies will be told’ to allow for times when not living there. The word ‘always’ is important in the given question.

2. Danon says:

Unfortunately, my answer does not ignore the given information. The information does not discount for an individual owning and living in two places.

By your estimation, an individual could only lie or tell the truth if they are actually in there house when they give a statement. A person could spend equal time in two houses, and give statements based upon that premise. The puzzle would have had to state that an individual could only live in one kind of house, thus preventing the possibility of a paradox. As it stands right now, due to the nature of the first persons statement, he could have said anything. Including my answer.

3. Let us start with your supposition that #1 has two houses: On day 1 he lives on the odd side, and is sworn always to lie. Another way of saying ‘always tells lies’ is ‘never tells the truth’. Therefore he can never move into a house on the even side because he can never tell the truth as he is already a sworn liar. Similiarly if he first moves into the even side, he can never lie and thus never move onto the odd side. This is the pure logic which prevents anybody from, as you suggest, living on both sides of the street.

In any case, #2’s statement that somebody else claims to be living on the odd side must be a lie because a sworn liar (odd) can never tell the truth about where they live. Because of this, #3’s claim that #2 is a liar is correct, so #3 is sworn always to tell the truth and must live on the even side of the street.

4. Danon says:

Hence the premise behind the paradox. He can, and does, do both. But #1 doesn’t matter in the grand scheme, we care about #’s 2 and 3. And based upon a paradoxical statement, #3 is ultimately indiscernible.

5. M says:

Nah…

12. Ronda says:

Yep, I got it, and I liked it. It was not a gimme–made me think–but doable.

13. Kristian says:

I didn’t get the whole ‘murmur too soft to hear’-thing. I didn’t consider how #2 got their information. I couldn’t find any inconsistency with only the statements from #2 and #3.

Didn’t solve it. You got me this week, prof 🙂

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