That semester, Gates was fascinated with a math problem called pancake sorting: How can you sort a list of numbers, say 3 4 2 1 5, by flipping prefixes of the list? You can flip the first two numbers to get 4 3 2 1 5, and the first four to finish it off: 1 2 3 4 5. Just two flips. But for a list of n numbers, nobody knew how to do it with fewer than 2n flips.
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