Uncovering the Truth: A Logical Approach to Determining Football Game Time

[tgt]

Homework Statement

You ask your friend if the football is on 9pm or 10pm. He sometimes tells the truth and sometimes doesn't. What should you ask him so that you will be certain which time the football will be on?

The Attempt at a Solution

ASK: Is it true that 'You are telling the truth if and only if the football is on at 9pm?'

It seems too clumsy

 

[Avodyne]

If I asked you if football is on at 9 PM, what would you tell me?

 

[tgt]

If I asked you if football is on at 9 PM, what would you tell me?

Practically, I don't see the difference between your question and the question: Will the football be on at 9pm?

 

[getitright]

Trick question. If he doesn't tell the truth all the time there are no questions to verify the truth of the answer. I would suggest waterboarding him.

 

[CompuChip]

You can just ask him if it is on at 9pm and watch the television. You will know whether he lied or not.

 

[tgt]

Trick question. If he doesn't tell the truth all the time there are no questions to verify the truth of the answer. I would suggest waterboarding him.

So you are assuming he might lie in the indirect question as well? In which case we have no hope? i.e Avodyne is probably assuming he answers the implication honestly?

But there is an answer to this question?

You can just ask him if it is on at 9pm and watch the television. You will know whether he lied or not.

That's cheating. The goal is to ask one question and from his answer, know for certain whether the show is on at 9pm or not, no matter if he lies or not in the answer.

 

[elliotician]

Is it true that you are lying and the football is on at 9?

If he is telling the truth he will say no since he is not lying as the statement is always false when he is telling the truth.
If he is lying then he will say yes if its on at 9 and no for 10.

Using the and logical operator means he will always answer no when telling the truth
So we know if he says yes that the football is on at 9. However we would then have to ask another question to find out if the football is on at 10.

Is is true that you are telling the truth or the football is on at 10?

If he is telling the truth and says yes then we know the football is on at 10
If he is lying he will always answer no since the statement is true when he is lying.

 

[tgt]

Is it true that you are lying and the football is on at 9?

If he is telling the truth he will say no since he is not lying as the statement is always false when he is telling the truth.
If he is lying then he will say yes if its on at 9 and no for 10.

Using the and logical operator means he will always answer no when telling the truth
So we know if he says yes that the football is on at 9. However we would then have to ask another question to find out if the football is on at 10.

Is is true that you are telling the truth or the football is on at 10?

If he is telling the truth and says yes then we know the football is on at 10?
If he is lying he will always answer no since the statement is true when he is lying.

How do you know that he is lying or telling the truth to the questions you made up?

 

[elliotician]

If he says yes in the first question you know he is lying so its on at 9.
If he says yes in the second question you know he is telling the truth so its on at 10.

If he says no in either case your at a dead-end, you would have to keep asking both questions till you got a yes. May be a better way but I am stumped.

 

[getitright]

If he says yes in the first question you know he is lying so its on at 9.
If he says yes in the second question you know he is telling the truth so its on at 10.

If he says no in either case your at a dead-end, you would have to keep asking both questions till you got a yes. May be a better way but I am stumped.

Now we're back to the whole waterboarding thing again.

 

[CompuChip]

Now we're back to the whole waterboarding thing again.

Which, apart from easier than trying to cook up tricky questions, is also more fun!

 

[Bohrok]

This might help out a bit
http://books.google.com/books?id=Je...X&oi=book_result&ct=result&resnum=10#PPA69,M1