An auditorium with 200 seats, numbered from 1 to 200, is filled to capacity. A speaker, who happens to be a mathematician, steps up to the podium overlooking the audience and pauses for a moment. “You know,” she says, “I’m thinking of a rather large whole number. Every seat number in this auditorium evenly divides my number, except for two of them — and those two seats happen to be next to each other.”
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