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: An idea without the math. again by Leming)

With the process of moving to the box that coresponds to the number just found:

One person will fail 50% of the time.

The second person will fail, upon success of the first 15.09% of the time.

The third person will fail, upon success of the first two, 0.1524% of the time.

The fourth person will fail, upon success of the first three, 0.001555% of the time.

Cumulative: 65.25 % failure rate.  34.75 % success rate.

Posted by Leming on 2007-01-30 12:05:37