A prisoner is up for execution, and comes before the king. The king says "I will commute your sentence, under the following condition. My daughter is the tallest woman in the land. I will show you every woman in the land, one at a time, and you must choose my daughter when you spot her. You can inspect each woman once, and only once. After inspecting each woman, I will ask you if she is my daughter. Either you will guess that she is not my daughter, in which case I will bring in the next woman, or you will tell me she is my daughter, in which case I will tell you whether you are right (you live!) or wrong (you die!)."
The question is: what is the strategy that the prisoner must employ to maximize his chances of winning? And what are his chances?
I don't know what the answer is to the first question, but (as a hint), the answer to the second question is 1/e. I think