# A discrete mathematics question about logic?

1. Feb 19, 2015

### sinashan

Hey guys
here is the question i'd appreciate if you could help me with it:
it says that no one dies in planet X,some spies of planet Y were captured by planet X's police.They are so professional that won't say anything to police so their inspection will go on forever and their inspection has no order.
In the inspection room there is only a lamp with a key on the wall and just the spies can turn it on and off(not the police)
Police has one condition to let the spies go:if any of them says that all spies have been inspected at least one they'll be free and if he's wrong they'll all be executed!!!
Suppose that you are one of those spies and you make a plan with your friends that one of the spies can find out if all of them have been inspected at least once.what will your plan be if:
a)you know that the lamp was off at first
b)don't know whether the lamp was on or off
also you make all your plans before getting captured and after that you have no conncetion to your friends.
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again thank you for your help it's a question related to logic in discrete mathematics

2. Feb 19, 2015

### Ray Vickson

3. Feb 19, 2015

### sinashan

what do you mean?

4. Feb 19, 2015

### Ray Vickson

What I mean is explained thoroughly in topic 4 of the "pinned" Post "Guidelines for Students and Helpers", by Vela. It appears at the top of the topic listings in the Forum.

5. Feb 19, 2015

### Zondrina

No one dies on planet X though. I don't see why anyone is getting executed in the first place, even if they did lie.

Seems fishy.

6. Feb 19, 2015

### sinashan

no they were spying that's because they're gonna be executed.although i think the first sentence of problem is just a distraction

7. Feb 20, 2015

### HallsofIvy

Staff Emeritus
What in the world does the lamp have to do with anything?