Say there are 5 guys at a party and they're all wearing silly hats. They decide to trade hats, and so they all throw their silly hats into a pile in the middle of the room. Then they close their eyes and randomly all grab a silly hat from the pile at the same time and put it on. How many ways can these 5 guys pick hats such that none of the 5 guys have picked their own hat?
How about for 10 guys?
How about for n guys?
The best part about this is that there's pretty much no way to Google the answer, or even to Alpha the answer, or even Maple the answer. Doesn't it feel a little weird to be asked a question like this where you can't just say "I don't know, but Google does?"
Peace out.
[[ It took me about two hours to figure this problem out, just sitting and thinking. Major props to you if you figure it out faster than that - you should consider a math major ]]
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