20-CS-110-001 Introduction to Computer Science Fall 2010

Dashing Courtier Puzzle

    In an arena in ancient Rome there was constructed a stage with three pairs of doors. Behind one pair were two tigers (one per door), behind the middle pair were a beautiful lady and a tiger, and behind the remaining pair of doors were two identical beautiful twin ladies. A courtier was then brought in with hopes of choosing a beautiful lady to be his wife from behind one of the doors. The particular way this was done is as follows: first he would choose a pair of doors. Then he would choose one of the pair. That door would be opened. If it's a tiger, he gets eaten and that is the end of the story. If it's a beautiful lady the door would be closed and the lady and partner would be randomly rearranged behind their doors (with probability 1/2 they would switch). Then the coutier would choose one of those doors. If a tiger - end of story. Otherwise a random rearrangment again and another choice of door by the courtier. This time, if a lady, they would marry. What is the probability that the coutier would survive and marry?
       
    solution