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Fatal Guess (Posted on 2007-01-29) Difficulty: 3 of 5
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?

No Solution Yet Submitted by atheron    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): An idea without the math | Comment 5 of 14 |
(In reply to re: An idea without the math by Gamer)

I like the idea.  However, I tried a test of 10 boxes for 10 people.  Only 9 times out of 30 did I have a loop of 5 or less.  This is 30% and may be a solution, but my simple test did not mirror the mathematical results of 50%

I then extended my data and got 19 successes out of 60 = 32%

Edited on January 29, 2007, 4:23 pm
  Posted by Leming on 2007-01-29 16:10:29

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