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        riddles >> medium >> Truther or liar?
        
(Message started by: BenVitale on Jun 18^th, 2009, 12:10am)

Title: Truther or liar?
Post by BenVitale on Jun 18^th, 2009, 12:10am

Every member of the Luncheon Club is either a truther, who always tells the truth when asked a question, or a liar, who always answers with a lie.

When I visited the club for the first time, I found its members, all men, seated around a large circular table, having a lunch. There was no way to distinguish truthers from liars by their appearance and so I asked each man in turn which he was. This proved unenlightening.

Each man naturally assured me he was a truther.

I tried again, this time asking each man whether his neighbor on the left was a truther or a liar. To my surprise each told me the man on his left was a liar. Later in the day, back home and typing up my notes on the luncheon, I discovered I had forgotten to record the number of men at the table. I telephoned the club's president. He told me the number was 37.

After hanging up I realized that I could not be sure of this figure because I did not know whether the president was a truther or a liar. I then telephoned the club's secretary.

"No, no," the secretary said. "Our president, unfortunately, is an unmitigated liar. There were actually 40 men at the table."

Which man, if either, should I believe?
Suddenly I saw a simple way to resolve the matter.

Was it 37 or 40?

Title: Re: Truther or liar?
Post by towr on Jun 18^th, 2009, 1:30am

[hide]You can't have two truthers or two liars next to eachother; so they need to alternate, which is only possible if there's an even number[/hide]

Title: Re: Truther or liar?
Post by rmsgrey on Jun 18^th, 2009, 8:34am

Is it inconsistent for there to have only been 4 men there rather than 40?

Is it the case that the secretary's statement about the club president's veracity is a separate answer under the club rules, or is it part of a compound answer "[the president's a liar] && [there were 40 diners]", or not an answer at all?

Of course, if the secretary was seated next to the president at lunch, that would settle things...

Title: Re: Truther or liar?
Post by Grimbal on Jun 19^th, 2009, 12:57am

I also have a problem with systematic liars that give combined answers.

In fact, the secretary said 4 things:
- No, no (presumably to the question whether the president's statement was true)
- Our president is an unmitigated liar
- This is unfortunate
- There were actually 40 men at the table

So if this is a combined statement, it could be a lie whatever the number of members.

And the question remains whether BenVitale could be trusted. I find this story of a club having only truth tellers and systematic liars a bit suspicious. I am not sure that club really exists. ;)

Title: Re: Truther or liar?
Post by BenVitale on Jun 23^rd, 2009, 3:37pm

How about you pick a person. Then, assume he tells the truth. What is then true of the person on his left? Pick a person, assume he lies. What is true of the person on his left?

Title: Re: Truther or liar?
Post by rmsgrey on Jun 24^th, 2009, 10:17am

on 06/23/09 at 15:37:47, BenVitale wrote:

How about you pick a person. Then, assume he tells the truth. What is then true of the person on his left? Pick a person, assume he lies. What is true of the person on his left?

Exactly what Towr referred to in his hidden reply?

Title: Re: Truther or liar?
Post by BenVitale on Jun 24^th, 2009, 11:16am

on 06/24/09 at 10:17:59, rmsgrey wrote:

Exactly what Towr referred to in his hidden reply?

Oops! Sorry. He did. I should have looked first.

Title: Re: Truther or liar?
Post by chronodekar on Jun 25^th, 2009, 4:37am

[hide]In this event, 40 is the ONLY reasonable choice. (reason given by towr).[/hide]

For sake of argument, if the president told us that the number of people at the table was 38, is it even possible any more to figure out how many people were there ?

I can't think of anything.

-chronodekar

Title: Re: Truther or liar?
Post by wolfiewolfie on Jul 19^th, 2009, 7:11pm

One possible solution could be that the president is actually telling the truth.

There were 37 MEN at the table.

36 members and the story teller = 37

Obviously he is not included in the truther/liar problem so he went through 36 members, an even number, and as towr has said, an even number would work.

The 40 solution would not work as he was at the table, and he was not a member, which would mean that there were 39 members at the table.