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        riddles >> what happened >> murder mystery game #8
        
(Message started by: BenVitale on Jun 19^th, 2009, 11:49pm)

Title: murder mystery game #8
Post by BenVitale on Jun 19^th, 2009, 11:49pm

Two suspects are brought in for questioning after a murder.
The only statements the police can get are these:

Suspect A: I am innocent.
Suspect B: Exactly one of us is telling the truth.

Which one is the murderer?

Title: Re: murder mystery game #8
Post by towr on Jun 20^th, 2009, 4:16am

There is no way to tell.

If I say "this sentence is untrue", is that sentence true or not?
Whether a suspect is a murderer depends on whether he murdered someone, not on an invalid assumption that a number of statements should be in some way logically consistent.

If suspect A is the murderer, A is lying, and B may either be lying or telling the truth. If B is the murderer, then A is telling the truth and B can neither be telling the truth nor lying; but he'd still be the murderer just the same.

Title: Re: murder mystery game #8
Post by Grimbal on Jun 20^th, 2009, 4:47am

I agree. The problem is people don't explode, or "switch off" when they are about to tell a sentence that can be neither true nor false. People can say "I am lying".

I would add that A gives a much more typical answer for an innocent than B.

Title: Re: murder mystery game #8
Post by BenVitale on Jun 20^th, 2009, 12:18pm

Argument:

B's statement can either be true or false.

(1) If B's statement is true, then B is the only one being truthful, hence A is lying.

(2) If B's statement is false, then both are lying.

The opposite of "Exactly one of us is telling the truth" is 'both of us are lying'

Hence, in (1) and (2) A is not innocent. Either way, A is guilty

Title: Re: murder mystery game #8
Post by towr on Jun 20^th, 2009, 2:13pm

on 06/20/09 at 12:18:22, BenVitale wrote:

Argument:

B's statement can either be true or false.

And it can also be nonsense.
By not taking that into account the argument fails.

If I shoot you; and, well, let's just suppose you don't die, and a policeman comes by. You say "That bastard shot me", I say "Exactly one of is telling the truth". Should the police officer really, honestly, conclude that you're lying?
How does anything either of us say change the reality of what happened?

Title: Re: murder mystery game #8
Post by BenVitale on Jun 20^th, 2009, 3:44pm

on 06/20/09 at 14:13:45, towr wrote:

You're right ... my argument is not valid.

So the problem is undecidable?

Title: Re: murder mystery game #8
Post by Grimbal on Jun 20^th, 2009, 4:18pm

I think so. The problem being that a logical sentence shouldn't refer to itself. If it does, it is not necessarily true or false. It can be both or neither. If A is innocent, it is neither.

on 06/20/09 at 14:13:45, towr wrote:

If I shoot you; and, well, let's just suppose you don't die, and a policeman comes by. You say "That bastard shot me", I say "Exactly one of is telling the truth". Should the police officer really, honestly, conclude that you're lying?

Most likely he would say "yes, and it is not you!". His reasoning would be "smartass answer" = "suspicious behavior" = "he shot the man", without bothering about the logical aspect of the question.