Today I am off to Manchester today to host part of QED – if you see me there, please wave. OK, 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?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

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 USAhere). You can try 101 of the puzzles for free here.

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Got it!!…. Or maybe I live in an odd numbered house!?!

Took me about 5 mins. I found it v tricky!

I first came across this in an old old Doctor Who episode (in the 70’s) – this has an extra twist but basically the same – got it in about 1 minute

Pyramids of Mars w/ Tom Baker and Elizabeth Sladen

About 30 seconds

Got it in 1 second

TMT, 29 Acacia Terrace

I think it took me about three minutes, but then realised it should have taken me only half a minute. It’s about what people in this street can say and what not.

30 seconds of thinking. Nice puzzle

Got it!

Nice one. I think I got it in about 3mins of jotting down…

I jotted it down as well. It seems to make it easier to solve this type of thing.

So much easier to write it down with pencil and paper…here the PC doesn’t help me at all!

15seconds I hope I in it right

It’s easy enough to verify. There are no ambiguities here.

“There are no ambiguities here.” For a change.

I am afraid you are wrong about ambiguities. Richard makes a statement about people who live in houses in the next street, but what about residents of flats, condos, chapel conversions etc?

I lived in Toronto. I have a bachelor suite. When I invited someone to come here, I tell them to come to my house, as all Torontonians do. No ambiguity is perceived.

All Torontonians tell people to go to your house? Does it get a bit crowded?

It does, but my hamster devours them all!

A couple of minutes with pencil & paper. Quite a nice puzzle.

Got it, 10 secs if that.

Nice puzzle. I think I managed in under a minute.

I believe I got it right off.

An actual puzzle! Satisfying when you get the answer, too. I guess half a minute to a minute.

I knew how to fix it within about 10 seconds. Had to write down stuff in order to not get confused. Once written down, it worked and I know the answer. 30 seconds in total.

Liked this one! It is one that needs a bit of thinking to get to the answer. And there is no alternative I think.

about a minute

it took me about one minute because i first started thinking at the wrong end :-)

We can also tell if person 2 is living in an odd or even numbered house… can you also tell in what kind of house Person one lives?

Yes, I was also starting at the wrong end, and kept thinking about it. Once I realised that, it took me less than a minute.

You cannot tell where first or second person live, only the third person

On the contrary, once you know if the third person is lying or telling the truth, you know the veracity of the second persons statement as well.

If you know whether they’re lying or not, you know where they live.

I also started at, well maybe not with the wrong end, but with a wrong twist. Then after a minute or something, I understood how to do it, then it was just “snap”.

A couple of minutes. Nice one!

under a minute. Easy one this week

And they say Canadians don’t have a sense of humour?

How wrong can you be?

Got it in just a few seconds.

Are they Cretans by any chance?

I feel really stupid now, because i am struggling with this one! To me at least it seems that either answer is logically possible.

Incidentally are we assuming that what the first person said was some sort of statement (true or false) about what kind of house s/he and/or the others lived in? I realise it shouldn’t matter, but am worried that it might.

STUPIDITY UPDATE: I now realise that the first person was answering a question about which house they lived in so no assumptions necessary. I can still come up with either answer, though. I could spell out my stupidity…?

Imagine that the person lives on the odd side. What would her/his response be? Now, imagine that the person lives on the even side. What would her/his response be?

Surprisingly quick! These ones normally take a couple of minutes to think through but I saw the key concept once I finished reading and the answer was easy from there. About a min in total.

Few minutes. I like this one, it’s not too complicated.

Nice one this week! 1 min

Got it, took about 1 minute

Well, after thinking about it for another minute, it seems there may be multiple right answers.

No, there aren’t.

Yes, there are.

Only if you assume that there are dwellings on this street that are not houses.

No, you can also take into account paradox’s.

I am still stumped. Here’s how my clumsy mind is going about things.

The first person (A) must live in an even-numbered house, because if A mumbled “odd” A would be lying, and if A said “even” that would be true. Nevertheless, A could have lied or told the truth.

That means that what the second person (B) says could also be true OR false (casting aspersions on A’s veracity but not changing the fact that A lives in an even-numbered house).

Which in turn means that the third person (C) could be

1) truthfully claiming that B is lying

2) falsely claiming that B is lying

3) truthfully claiming that B is telling the truth

4) falsely claiming that B is telling the truth.

And as C could either be making his/her claim truthfully or falsely, we can’t determine whether C lives in an even- or odd-numbered house.

I must be starting at the wrong end of the stick or something.

Further musings occur to me… another post i think.

Almost, but not quite. Don’t think about where A lives, only about how many answers A can give.

Thanks, Bart. Got it now! Wow, i really like the way the design of this puzzle hid the solution from me for so long! So all those doubts were just totally irrelevant? Is there a word for this? (For this kind of puzzle, i mean, not for my blindness!)

In my experience, it’s the type of thing that you have to be in the right mood for.

The “Cretan paradox” seems relevant: the Cretan who says “all Cretans are liars” – or, even more concisely, someone who says “I am a liar”.

We have to assume (i think) that A, B, C know that we know the unusual fact about people from odd-numbered houses and people from even-numbered houses, and therefore any statement about house numbers is an indirect statement about truth-telling.

So we have an indirect Cretan paradox, as B is effectively saying “A is a liar” – but we don’t know what A said; and C says the same thing about B.

So as far as I can see, C can still either be telling the truth or lying, so we can’t tell whether C lives in an odd- or even-numbered house:

A lying, therefore B telling the truth, therefore C lying, therefore C ODD

A telling the truth, therefore B lying, therefore C telling the truth, therefore C EVEN.

Perhaps Danon is having similar doubts? Or am i just being especially dense this morning?

That reminds me of Star Trek: “I, Mudd”, where Harry Mudd says “I am lying”.

You’re running too fast. Think of A. Assume for a moment that A lives on the odd side. How many possible answers can A give?

Now assume that A lives on the even side. How many possible answers can A give?

How do these answers compare with each other?

Once you know that, you will know that B is either a liar or telling the truth. Once you know that, you will know what C’s answer *must* be and therefore on what side of the street he lives.

“am i just being especially dense this morning?” heh.

I got there from your previous hint! Thanks though for explaining it so patiently!

I am still very happily musing on the way the puzzle misdirects you away from the various truth-claims towards wondering what side of the street their makers live on!

So much more satisfying than last week’s. Pleasurable to lose yourself in the trees and then suddenly the wood whacks you between the eyes!

Hehe, you almost make me feel guilty. Fortunately, there is no reason. I merely said what you should do, I didn’t suggest any answers ^_^

About ten seconds. Phew! I start Friday feeling capable of anything. You have no idea of the power of these Friday puzzles…

Well, just got it, thanks to Barts hint. Don’t think I would ever have got it otherwise. What a numpty I am!

Catherine, you are right, although I now start Friday realising I am as stupid as I thought I was.

Took me about 5 mins because I started writing a matrix of all possible cominations of the people on the street. Then I realised this was completely unnecessary when I actually started thinking it through.

About 30 seconds, I think- flash of inspiration…

Started writing down the options for A and then it clicked. About a minute. Nice puzzle.

Obvious puzzle is obvious. Solved while reading.

nicely solvable during the wake-up coffee, likeable logic, but what about the people on your street are they always truthful?

Got it so quick, I knew the answer before I read the puzzle. In fact, I was thinking the answer as I fell asleep last night. To be completely honest, I was born knowing the answer.

My first words to my dear mother were ‘Mother dear, the answer to the puzzle will be…’ (no spoilers!)

My house number is 48, by the way. Honest. No word of a lie. Would I lie to you, dear friends?

Got it by writing it up, about 2 minutes.

By the way: The webcomic “The Order of the Stick” has the correct solution for every “one always lies, one always tells the truth”-problem:

http://www.giantitp.com/comics/oots0327.html

Are the people posting all of these comments telling the truth or are they lying?

Lets have a debate ……

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Couple of minutes. The time it takes will heavily depend on whose answer you choose to think about first (I picked the second guy, because he was first to give an actual hint, stupidly).

very easy, but cool thanks Richard

Got it, after a bit of discussion! 2mins :)

It took a couple of minutes. Of course, I was making it harder then necessary.

Very quickly, less than a minute. But here’s a twist: how could the 3rd person know what color hat he was wearing?

By asking “if I asked you what colour my hat was what would you say?”

solved in 10secs

About a minute. At first I thought number one was irrelevant, then realised he is the key. (In a way..;)

Very easy this week – under 30 seconds.

Hooray! I was really struggling until the solution clicked.

I think this one is actually easier than it seems. Less than a minute.

Lying is not the same as being wrong. If a person truly believes that 1 + 1 = 3, he is honest when he says so. These puzzles have to have an added premise that all people have absolute knowledge and are never wrong

In the present case, the first person was said to mumble “too soft to hear”, so what the second and third persons say is not necessarily relevant to what the first person said, since presumably they would have the same trouble hearing it

The way I’ve usually seen this is that the people speak a foreign language, hear everything said and (obviously) know what it means, which would rule out this particular ambiguity.

Fascinating, but irrelevant old boy.

Is it irrelevant?

Person 1 says “I live in an even numbered house”

Person 2 mishears, thinks 1 says odd, and says so.

Person 3 is then wrong to call 2 a liar, but did he make the same mistake as person 2? Did he also mishear it as “odd” and lies when he calls 2 a liar, or did he hear person 1 correctly and thinks he is correct in calling person 2 a liar?

The way the question is phrased, you just can’t tell.

There is also the possibility that person 1 doesn’t know what odd and even numbers are, in which case all bets are off

Tedious and irrelevant

For anyone who still isn’t sure of the answer:

Would anyone ever answer that they live in an odd numbered house?

15 secs. A snap.

Of course there are ambiguities. There are ALWAYS

ambiguities. Nature of language. As Clinton said re

his testimony on Ms. Lewinski (when he said under oath

that “There is not a sexual relationship…between us…”)

“It depends on what the meaning of “is” is.”

(His testimony was true in that she was not currently his

lover, false in that she had been recently.)

But a reasonable, “most probable” reading of this puzzle

would imply that everyone on the next street lives in either

an odd-numbered dwelling or an even one, that all Odds lie

and all Evens tell the truth, and that they KNOW whether

their dwelling is odd or even so they are not confused or

mistaken in their testimony. Right?

In which case it’s an easy puzzle, and an old one – I think

Sam Lloyd originally posed one much like it.

One key assumption is that person 3 either:

A Heard #1’s answer

B Knows where #1 lives and assumes #1 did not lie

C Knows that all odds lie & all evens tell the truth AND understands logic well enough to reason out the truthfulness of #2’s statement.

I have no idea where it originated. I first read it in Raymond Smullyan’s “What is the name of this book?”, which is filled with great logic puzzles. One of my favourites (of the books that weren’t written by Martin Gardner, that is)

about 20 seconds… I think…

Karl’s assumptions are incorrect. I can’t elaborate until Monday.

Karl, RW always says we aren’t to give out any of the answer until Monday. Did you not read that?

Yes, I did read that. I assume you are aware that I did not actually give out any answer, but instead are chastising me for coming too close to revealing an answer without actually doing so.

I will concede that perhaps I have gone too far, but I did not really go any further than many others have here and often do in these.

I look forward to your elaboration on Monday.

Wow, Beaky

I will be on tenter hooks till Monday, when you reveal all.

Easy. Less than 30 seconds. Must be because I live in an even numbered house.

49 seconds.

Am I the only one that thinks it’s all about person B’s statement?

I must be thick so…

:-(

It’s all about B’s and C’s statements.

Yes, it’s easier than appears at first. You have to read every word of the puzzle carefully and then you get an ah-ha moment.