Five prisoners are going to take beans from a bag with 100 beans. They will do it one prisoner at a time, and only once each. No communication is allowed between them, but they can count the beans left in the bag. All prisoners who end with the largest and the smallest number of beans will die.

Who is most likely to survive?

Assume:
1. they are all smart people.
2. they will try to survive first and then try to kill more people.
3. they do not need to take out all the 100 beans.

Still assuming the prisoners don't know which order they are in...

After an exhaustive process of logic working out scenarios between the extremes of 1 and 20 beans (no prisoner takes more than 20 or 0 - assured death) they realize that counting the beans leads to all prisoners choosing either the max. or the min. (and all dying). They must arrive at the following logical strategy:

"When the bag of beans comes to me, I will not count, I will just reach in and grab a handful."

This is the only strategy which approches a 3/5 probability of survival for each (except for coincidences at the extremes).  All are then equally likely to survive.

Posted by Eric on 2005-11-30 02:00:36