# Answer to the Friday Puzzle

39

On Friday I set this puzzle…..

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?

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

Well, the first assumption has to be that I am telling the truth.  If that is not the case, then all bets are off and there is no answer.  However, assuming this is the case, there must have been
(1) a mixture of liars and truth tellers around the table and
(2) an even number of people around the table.
(3) they alternate liar – truth teller around the table
Otherwise, everyone would not be able to say the sentence ‘I declare that the man on my left is a liar’.

So, John must be the liar.  Did you solve it?  Any other solutions?

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. Gib says:

Yep, that’s the solution I got straight away.

• AMWhy says:

Ditto. I compared 3 people and 4 people to see which would complete the circle – 4 worked, hence all even numbers work. Answer can’t be 11 so must be 8 people.

2. Eddie says:

I prefer puzzles for which the solutions are not based on assumptions.

That’s puzzling, Eddie. I’d assumed that they were the kind that you liked.

• Dave says:

Sigh. The only assumption was that it was an actual puzzle. Hardly a stretch of the imagination for those of us with more than a handful of brain cells.

3. Damocles says:

Yes. Not much else to say really.

4. -M- says:

Yes, got it.

5. Dave says:

Got it

6. Mickey D says:

Yes solved it!

7. Anders says:

Actually You couldnt be a liar. Think about it, if you were an “always liar” and was member of a club, you could never actually say “I am a member of this club..”, that would entail telling the truth. The only solution is that you are a member and telling the truth, or a liar in your spare time, but if so, you dont have to be either/or liar/truthteller, since you dont have to qualify for the club.

• Lazy T says:

I always tell the truth, am a member of the club, It really does exist.and there are an infinite number of members.

8. Roy Gillett says:

Depends how you view the original statement. If we apply the truth/lie criterion sentence by sentence, then it has to all be true. But if we apply the criterion to the entire statement then it could have elements of truth in it (“I am a member of a club”) but be *overall* a lie–that is, Richard is a member of the club but didn’t get the phone call.

• Anders says:

The wording was that half the members ALWAYS lie, which I take to mean that everything they say must be a lie.If you are a member of this club then, stating so would be an honest statement that stands on its own, and therefore cannot be said by someone who ALWAYS lie. Such half-true, half false statements would render a person dishonest and untrustworthy, but not a perpetual liar. In a way, that last category of liar is kinda trustworthy, because you could word a question such that he or she unwtittingly tells the truth by lying(as is common in puzzles like this)

9. Myk Dowling says:

It’s only definite if all members present are male. Any women present would be skipped in the statements. Your privilege is showing, Richard.

• Berber Anna says:

Well, assuming this is a traditional British club, all members would have to be male. Not so much Richard’s privilege, as society’s.

• Myk Dowling says:

Richard’s showing his privilege by not even considering the possibility that club members could be women.

• Henry Ruddle says:

It is also possible that all of the truth tellers are women, and all of the liars are men, which proves that Richard is one of the liars because my ex-wife must have written this puzzle for him.

10. Berber Anna says:

Yep. Had to draw it up (I’m horrible at figuring out these things without pen and paper), but that’s the answer I got.

11. Pedro says:

How do you know that either John is a liar or Tim is a liar? Both could be lying. In fact, a competent liar would not change the parity of the number of people around the table, only the number itself.

12. spiderabc1 says:

My first answer was 8 (John being the liar) but this was based on seating arrangements. If 11 people then an odd ratio of “man to left”. Also considered 4 males and 4 females in the seats.

13. Or the first member to call was a liar…

14. Karl Withakay says:

Is the statement “Either John or Tim was lying” stating a known fact, or is it a conclusion made by the puzzle presenter based on the stated conditions?

If it is a conclusion, it may be an erroneous conclusion. We could not know that Tim was not (also) a liar. Tim may not have been at the dinner (and therefore lying about being at the party), or there may have been a different even number of people at the table.

Also, there is the question of whether “I was at the dinner and there were 8 of us there”. is two statements of fact that each must be false if made by a person who “always lies” or is a single logical statement that becomes logicaly false if either condition is untrue.

15. Anonymous says:

What i got was a bit different. If the first caller always tells the truth ( i took that as a fact), and the members were sitting in a circular formation, everybody on that table could be liars. Because they say the person on their left is a liar and it goes on and completes a circle. Which makes everbody on that table a liar.

• But then they wouldn’t be lying. So they wouldn’t be liars.

• Anonymous says:

I thought the first one who called wasnt at the dinner or at the table. Because the way he tells it, it appears that he wasnt there.

16. Anders says:

That wasn’t my answer. My answer is that there were no men at all at the table, only women. Since “I declare that the man on my left is a liar” is always true if there is no man there at all, they were all truth tellers, and both callers were liars

The surgeon’s paradox I mentioned is the one where the surgeon turned out to be a woman.

• Dormouse says:

Good one.

Does everyone here already have a high paying job advising the UK and/or US government, or may I make a suggestion?

I thought that the surgeon was his step-father

17. I got the answer to the problem straight away, but noted there was a couple of holes in answering it as others have pointed out…. 1) Mr WIseman could be a liar, and 2, it very specifically switches to a gender based statement while all other statements don’t involve gender, so, you could inject women in the circle pretty easily.

So, I think the “intended” answer is not right because of the logical holes in the problem statement 🙂

18. Jerry says:

Yep, that was my answer and my reasoning as well.

19. Richard's Dorkings says:

Dormouse I don’t know about the US or UK, but I think that some of them are advising the Syrian Government

20. Wolf Martinus says:

I think that Richard is a liar and that means:
– he isn’t member in that club
– all the rest is also humbug

21. Chris says:

Also, all of the liars are men, and all of the truth tellers are women, or the group is all men.

22. norbert the vague says:

I always get sidetracked into what a “lie” is. Telling the truth is understandable – it is a statement in agreement with reality. So a lie is not in agreement with reality. But there is an infinite number of ways to lie. Some have approached this above by introducing women as possible club members. What if the liar is asked a question such as “what colour is my hat” and replies “elephants eat lampshades?”

The point is this: a real liar is someone who intends to deceive you. They may do this by telling the truth. Example here: http://www.youtube.com/watch?v=U_eZmEiyTo0

• Anders says:

I sort of agree. There is also the question of knowledge. To me, a lie is a statement intended to be false, while telling the truth means the speaker thinks what is said agrees with reality.

What your video shows is deceit, which as you say can be done by telling the truth or by lying, as circumstances demand.

but if I firmly believe that 1+1=3, I am lying when I say it equals 2

23. AntonioRabbit says:

Tim could also be lying. There may have been more than 8 people at the table.

24. Anders says:

Didn’t we have this recently? It feels awfully familiar

25. Anders says:

What does “the man on my left” mean, exactly? Is it “go down the table clockwise starting from me, and the first man you get to is the man on my left”, or does it necessarily imply a table neighbour sitting immediately next to me?

26. Thao says:

if i have just signed up but I really would enjoy to see a specific letter (Lorelei Lee’s) is there some place i can possibly watch it or obtain a copy somehow?