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Mathematics
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http://trickiestofall.blogspot.com/2011/07/people-combinations-room.html
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This reads like a computer problem. Where each person is assigned a value be it name etc and slowly stepped out like they are a numeral counting up. But with each person only showing up once the mathematical solution is factorial based if I recall correctly. So the solution for the number of combinations would be n! As for stepping them in and out one at a time well that's a hairier problem since they put no limits on the number of people.
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