You've been sentenced to death in an obscure foreign country which has a strange law. Before the sentence is carried out, two papers -- one with "LIFE" written on it and one with "DEATH" written on it -- are folded up and placed in a hat. You are permitted to pick out one of the papers (without looking), and if you choose the one with "LIFE" written on it, you are set free. Otherwise, the death sentence is carried out. But someone has substituted the paper with "LIFE" written on it with another one with "DEATH" written on it. You are informed by this person of what he has done and that you are doomed to die. You are not permitted to speak to anyone about this misdeed, nor will you have a chance to switch the papers yourself in time.

How will you avoid death?

(In reply to re: Common solution by gordo packard)

That's an excellent question.

You should try and take a quick peek at what's written on the paper before deciding whether to keep it or to get rid of it. If it says LIFE, then keep it and show it to the authorities. If it says DEATH, then get rid of it and go, 'oops'.

If the guy was truthful and both papers say DEATH, then you are saved.
If the guy was telling a lie and both papers say LIFE, then you are saved.
If the guy was telling a lie and he hadn't switched any paper and you draw LIFE, then you are saved.
If the guy was telling a lie and he hadn't switched any paper and you draw DEATH then you are decidedly unlucky and you will die. But since you don't know whether he was being truthful or telling a lie you are no worse off getting rid of the paper.

If the probability of his telling the truth or telling a lie is 50:50; if the probability of his telling a lie and writing LIFE on both paper and the probability of his telling a lie and not switching any paper is 50:50; if the probability of your picking 'this' paper or 'that' is 50:50, then you will be saved 7 out of 8 times (or 87.5% of the times) following this strategy.

I wonder if there is a strategy that delivers a 100% success rate.

Posted by Sanjay on 2003-07-02 09:08:41