[borisp]

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Here is a cooler problem, imo: show that the expected value of the # of people who get their hat back is 1, independent of n.

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Hmm, how about n(1/n)=1!
uA

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Ok, mr genius, show that the outcomes are independent. I know this is "intuitively obvious" but actually providing a proof is an altogether different matter.

And for once, I actually agree with Sklansky rigor. Tournament reseating is the perfect way to conceptualize this problem, for those who already have experience with poker tournaments.