I am a member of a club in which every member either always lies or always tells the truth. Yesterday I had a telephone call from a member who always tells the truth and he said ‘Some members have just had dinner around a circular table, and each member said ‘I declare that the man on my left is a liar’”. Ten minutes later I received another telephone call from another member called John, and he said “I was at the dinner and there were 11 of us there”. Ten minutes after that I received yet another telephone call from a member called Tim, and he said “I was at the dinner and there were 8 of us there”. Either John or Tim was lying. But who was the liar?

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

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About 30 seconds. Pretty sure I got it.

“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”

Er…?

Does anyone have the answer to next week’s problem?

Dave, of course. It’s a three parter: 75% purple, no, and battered eggs

30 seconds

jumbleguitar – If that reply was for me, it’s because there was a comment before mine replying to space_tiger stating the answer, but looks like it was removed!

Ditto … closer to a minute.

Please bear in mind that Richard admits that he is a member of this club, half of whom are liars……I think that he made the whole thing up.

(30 seconds)

One could easily adapt this into an ‘is Richard a liar or a truth teller’ puzzle.

Indeed. If Richard is a perpetual liar, does he belong to the club at all?

Dr. Wiseman meet Dr. Russell.

It seems to me to be a wrong assumption that half of the clubs members are liars

I’m think along these lines,

Yeah, I got the answer in a few seconds, with the caveat that if Richard is a member, there’s a 50% chance that there is no solution.

–Dave

About 3 seconds.

Think I have it only took a few mins feeling a little smug. My first one in a while.

I doubt such an odd club really exists!

Got the gist right away, and verified the corect case in a minute.

Simple. Got it as I read it.

Leaving out the basic flaw in all such puzzles (being wrong is not the same as lying) I actually thought this was a nice twist. I can think of two completely distinct answers that are both consistent with the wording of the question. About 5 minutes to think the whole thing through

About a minute to verify that my quickie answer was right.

Got it 1 second before it was posted

Two solutions, one requiring only a partial reading of the problem, and the other a bit more mathematical. 3 min total.

Solved. About half a minute to a minute. Very good – this one I liked!

30 Seconds and drawing a little circle

After drawing two circles, about 1 minute

Ditto. Had to double check.

I’m a member of that club, and I’ve never seen Richard there…..

I can’t solve this.

I solved this in a few seconds.

Only 1 of these statements is not a lie. ;)

About a minute but I was paying attention to a stupid Windows problem (triple tautology?)

Assuming Richard is a truthful member of the club, just a few seconds to get an answer.

But if Richard is not to be trusted, I’m not sure that there is an answer.

My conclusion too, unless I’m lying, or you are.

There is one answer in case Richard is one of the liars, and one answer if he is a truth teller. It can be solved

I forgot about Richard. Maybe I’m now wrong.

30sec. It becomes pretty obvious when you figure out how the table must be configured.

Though I’m sure the usual smart-arses will point out some problem with the wording, or some abstract solution that doesn’t really follow the ‘spirit’ of the intended problem.

Hmmm, I can’t rule out Richard lying…

I think on is impossible but I can’t rule out Richard lying…

If John or Tim are liars, and in this club the liars always lie, then how did Richard really know it was either of them on the phone? “Hello? Oh hi Steve.” “No, it’s erm… errr… John…” (or Tim, delete as appropriate).

Good point – unless of course their phones have Caller ID, which presumably cannot lie :)

This reminds me of the puzzle whereby in trying to escape a castle, you’re confronted by two doors, in front of each is a guard. You’re informed that one of the doors leads to freedom, while the other leads to certain death. You’re also informed that one of the guards always tells the truth, while the other always lies. However, there are no visual clues as to which door is which, or which guard is which. You’re allowed to ask one guard, one question before selecting a door.

Simple, you just ask one of the guards a question which you already know the answer to, like “Are you a man?”

As for Richards puzzle, all became clear on paper after a few seconds.

@Chris, so you’ve worked out which one is the liar… Now which door do you open?

I would ask: which door would the other guard say is the escape? Then take the other door.

Pretty sure I got the right answer. About half a minute to visualise both scenarios.

Pretty sure I got it! 1-2 mins

Sounds like a really shit club ;)

Got it, maybe 20-30 seconds? Of course there is always the possibility that the person asking the question is lying…

Got it, with one pretty big assumption though (as usual).

Sigh. Maybe I’ve seen too many “Puzzlers” in my life. Seems they are becoming more and more of the same recycled ideas.

and on the nth day all the monks left.

’bout 45 seconds

About 3 seconds including verification of my own reasoning.

I was at odds for all of a second or so, but I’ll give evens on me solving it in under 10 seconds.

if mr wiseman knows who is a liar and who is not a liar then there is no need to ask us the question. all he has done is withheld known information. that is discourteous.

if he does not know who is a liar and who is not a liar then it is possible that both tim and tom are liars. or both are telling the truth but the the number of guests fluxtuated during the dinner.

About a minute. When I started thinking about it, it was easier than I expected.

(My answer assumes that Richard is truthful and is giving an accurate account of what happened).

there is something known as parity ….

This is classic example of the Liar Paradox

The problem of the liar paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules

.

The simplest version of the paradox is the sentence:

This statement is false. (A)

If (A) is true, then “This statement is false” is true. Therefore (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.

If (A) is false, then “This statement is false” is false. Therefore (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.

However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is “neither true nor false”. This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle.

The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:

This statement is not true. (B)

If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true. Since initially (B) was not true and is now true, another paradox arises.

Another reaction to the paradox of (A) is to posit, as Graham Priest has, that the statement is both true and false. Nevertheless, even Priest’s analysis is susceptible to the following version of the liar:

This statement is only false. (C)

If (C) is both true and false, then (C) is only false. But then, it is not true. Since initially (C) was true and is now not true, it is a paradox.

There are also multi-sentence versions of the liar paradox. The following is the two-sentence version:

The following statement is true. (D1)

The preceding statement is false. (D2)

Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false. Therefore (D1) is both true and false.

Assume (D1) is false. Then (D2) is false. This would mean that (D1) is true. Thus (D1) is both true and false. Either way, (D1) is both true and false – the same paradox as (A) above.

The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements (wherein the last statement asserts the truth/falsity of the first statement), provided there are an odd number of statements asserting the falsity of their successor; the following is a three-sentence version, with each statement asserting the falsity of its successor:

E2 is false. (E1)

E3 is false. (E2)

E1 is false. (E3)

Assume (E1) is true. Then (E2) is false, which means (E3) is true, and hence (E1) is false, leading to a contradiction.

Assume (E1) is false. Then (E2) is true, which means (E3) is false, and hence (E1) is true. Either way, (E1) is both true and false – the same paradox as with (A) and (D1).

“This is a classic example of the Liar Paradox”

Not really. The classic Liar Paradox isn’t really a paradox at all. The classic statement, said by a person from Crete, was “All Cretans are liars”, which never was a paradox, since the negation of “all” isn’t “none”. The solution to that is that not all Cretans are liars, and the person speaking is (or is simply wrong)

The solution to this puzzle though, assuming Richard is a member of the truth telling part of the club, has nothing to do with liar’s paradoxes (or parity, for that matter). This is more of a surgeon’s paradox, if you will

Nice tits Katie

Anders

I know nothing of this surgeon’s paradox you speak about. All I know is that all surgeons are addressed as Mr.

TMT

Fair point Katie

It’s a little known fact that In Star Trek: The Original Series episode “I, Mudd”, the Liar paradox was used by the characters of Captain Kirk and Harry Mudd to confuse and ultimately disable an android

20 secs!

How easy! You got no phone calls because you are one of the members who always liie. And there is no club. And you are no Wiseman. Hello? What? A paradox? Nevermind.

Oo, I like this one, thanks, Richard :) If I’ve got the solution right, I’d say it took about ten seconds to confirm it (although there is another way of reading the question). Looking forward to Monday and finding out not only if I got it right, but if there are other ways of looking at it too :) Thanks again for another delightful brain workout :D

Immediate reminder of the door riddle in The Labyrinth ( http://www.imdb.com/title/tt0091369/faq )

about 10 seconds for an answer another 20 to double check myself.

Solved before I finished reading it.

PS. Are any of the responders above members of the club? And if so, which ones are they? And in which case are they truthies or liars?

Got it. This was a fun one.

“I am a member of a club in which every member either always lies or always tells the truth.”

LIAR!

Got it before Richard even thought of it.. OK, I lie. I wonder what it’s like going through life telling only lies. What a challenge. On the other hand, always telling the truth . . . ?

Wiseman is a phony – who is making good money off of his phoniness (and knows it).

At last Shdrake2 – a statement in this thread which is true without a doubt.

It took me 27 years to get the right answer, and the person standing to my left agrees with my perception of time, and does not in any way think that I might be dishonestly writing years rather than seconds. Thankfully although he’s a liar, he does trust my timekeeping.

I think it took me about three minutes counting the time it took me to find a piece of paper and a pencil, draw the relevant diagrams and test each of them.

It is not possible to solve this puzzle without falling asleep…

A couple of minutes. There are two possible answers, one of which indicates that all bets are off.

Yes, the first person who called always tells the truth. If there is no twist ^_^ i think i have solved it the first time i read it.