A group of terrorists have taken 100 men as hostages and numbered them as hostage 1,2,3...,100. The terrorists tell them that each one of them is asked to enter a room (one at a time) where there are 100 boxes each containing a paper with one number in it (each number is placed to a random box and each box contains only one paper).

Once a hostage is asked to enter a room he chooses 50 boxes to be opened and if he finds his number on any of the papers he will be escorted to a waiting room. If however the hostage fails to find his number all of the hostages are brutally killed. If all of the hostages succeed in finding their own number they all will be spared.

After telling this the terrorists give some time for the men to consider for an optimal strategy to survive. Once they have agreed on their strategy all communication is forbidden.

If all of the hostages choose 50 boxes at random their probability of survival is kind of weak (.5^100). What kind of strategy should they use to survive at least with 30% probability?

(In reply to re(3): An idea without the math. again. again by Leming)

That looks like the kind of number that would come up. I say this because Atheron specified "with at least 30% probability". 30% is an odd number, don't you think? He could have said 1 time out of 3 if the answer had been 34%, but he didn't. This makes me believe that the correct answer is just over 30%.

Posted by George on 2007-01-30 20:34:18