Wednesday, July 7, 2010

The Blind Date Bachelor

(Modified from a puzzle about a sultan and his harem I heard from Jon Huang.) The Blind Date Bachelor is the newest dating show, in which where there is 1 bachelor and 4 contestants trying to win his heart. He will meet each contestant for the first time on a blind date. At the end of the date, he must choose whether to marry her or never see her again. If he marries her, the game is over. If he rejects her, he is set up on a date with the next contestant and repeats the process. If he rejects the first 3, he marries the last one automatically. He is able to compare and rank contestants that he has already met, but will not know for sure who he likes best until he has met them all. It's very important that he marry the best one, or he will spend the rest of his life wondering what could have been. What strategy will maximize his chances of finding the best mate-for-life?

3 Bonus Questions: What is the probability of winning using the best strategy?  What if there are 5 contestants, not 4?  And finally, what if there are n contestants? 

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