Even Cooler Problem Involving e

[PairTheBoard]

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do you first pick some # that "must" go by, after which you pick the first one that exceeds the attractiveness of this group?


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DS -
Your strategy is to let a certain number of girls walk past you (all of whom you see perfectly) and then pick the first girl you consider prettier than any of the ones you let go by.

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I'm sure I've seen this before but I can't remember how it goes or what common sense type insight might cut through quickly to a solution. My first idea is to look at what happens if you let half the group go by before choosing the first prettiest. You then have half a chance of having a shot at the prettiest, but may still miss her. If I was ambitious I would grind through some math to calculate the probability exactly for this case. See how it goes, then do the same for a general cuttoff point and optimize. I'm not that ambitious though and it would be much more interesting if there is an intuitive approach that cuts quickly to a solution without a lot of math.

I wonder if there's a way to view this as somehow equivalent to the matching hats problem.

PairTheBoard