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.

I haven't spent too much time looking over the problem, but I have read the comments to see what others think.

One thing I noticed in the comments was the pervading assumption that the prisoners are aware of what number they are in the sequence.  That is, it seems to be taken for granted that they know how many people have already drawn from the bag, but I don't think that this information was explicitly (or even implicitly) given in the problem.

If the prisoners know how many have already drawn, then they know how many are left after theirselves, in which case it would make a significant difference how many beans they should take.

Posted by Peter on 2005-11-29 16:30:27