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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.”

As you’d expect, adjacent seats in the auditorium have consecutive numbers. Which two numbers was the speaker referring to?

 

 
Мне повезло: у меня случился инсайт, и процесс решения занял секунд 10. 
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