# Interesting logic problem

1. Jun 1, 2009

### tgt

1. The problem statement, all variables and given/known data
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?

3. 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

2. Jun 1, 2009

### Avodyne

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

3. Jun 2, 2009

### tgt

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

4. Jun 2, 2009

### 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.

5. Jun 2, 2009

### CompuChip

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

6. Jun 2, 2009

### tgt

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????

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.

7. Jun 2, 2009

### 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.

Last edited: Jun 3, 2009
8. Jun 2, 2009

### tgt

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

9. Jun 3, 2009

### 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 im stumped.

10. Jun 5, 2009

### getitright

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

11. Jun 5, 2009

### CompuChip

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

12. Jun 6, 2009