55 prisoners are on the deathrow. The warden gives them a chance to live. He puts 100 empty jars into room A and randomly puts 10 balls under the 100 jars. Each jar is either empty or contains 1 ball. In the other room, call it room B, the warden puts 100 empty jars, and a stack of 10 balls.
The warden then divides the group of 55 into two groups of 54 and 1. The group of 54 he puts into room A. The last prisoner goes into room B.
Each prisoner from room A will take turn looking under the entire 100 jars, but can not move or rearrange the contents. He then can go to room B and must say one of two possible words to the prisoner there. The 2 possible words are Lakers and Rule. Assume he can not convey any other information besides that word (so no facial expression, tone, body language, hand gestures, etc. ). Any attempt to convey extra information like remaining silent, concatenating words, or walking a certain number of paces before stopping in room B will get all prisoners killed immediately. The prisoner in room B will then have to reconstruct the permutation of the balls in room A.
If the prisoner in room B can successfully reconstruct the permutation in room A after the 54 turns, all 55 will live. Otherwise they will die.
The night before, the warden tells the prisoners this scheme, so the prisoners know that there will be exactly 10 balls under the 100 jars. They have 1 night to discuss a strategy. They are not allowed to bring any mechanical computational aid to the game (yes, abacus are out too). Assume that each prisoner has the mental computational skills of a reasonable average person.
1) What strategy would give the prisoners the best chance to live? Describe the strategy.
Question
bushindo
55 prisoners are on the deathrow. The warden gives them a chance to live. He puts 100 empty jars into room A and randomly puts 10 balls under the 100 jars. Each jar is either empty or contains 1 ball. In the other room, call it room B, the warden puts 100 empty jars, and a stack of 10 balls.
The warden then divides the group of 55 into two groups of 54 and 1. The group of 54 he puts into room A. The last prisoner goes into room B.
Each prisoner from room A will take turn looking under the entire 100 jars, but can not move or rearrange the contents. He then can go to room B and must say one of two possible words to the prisoner there. The 2 possible words are Lakers and Rule. Assume he can not convey any other information besides that word (so no facial expression, tone, body language, hand gestures, etc. ). Any attempt to convey extra information like remaining silent, concatenating words, or walking a certain number of paces before stopping in room B will get all prisoners killed immediately. The prisoner in room B will then have to reconstruct the permutation of the balls in room A.
If the prisoner in room B can successfully reconstruct the permutation in room A after the 54 turns, all 55 will live. Otherwise they will die.
The night before, the warden tells the prisoners this scheme, so the prisoners know that there will be exactly 10 balls under the 100 jars. They have 1 night to discuss a strategy. They are not allowed to bring any mechanical computational aid to the game (yes, abacus are out too). Assume that each prisoner has the mental computational skills of a reasonable average person.
1) What strategy would give the prisoners the best chance to live? Describe the strategy.
Link to comment
Share on other sites
Top Posters For This Question
8
1
1
Popular Days
May 26
42
May 27
9
May 29
4
May 28
2
Top Posters For This Question
bushindo 8 posts
soop 1 post
CaptainEd 1 post
Popular Days
May 26 2009
42 posts
May 27 2009
9 posts
May 29 2009
4 posts
May 28 2009
2 posts
57 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.