# AoPS Subset Problem

**Question description**

Let S be a subset of {1, 2, 3, 4...., 100}, containing 50 elements. How many such sets have the property that every pair of numbers in S has a common divisor that is greater than 1?

Brown University

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California Institute of Technology

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Dartmouth University

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Emory University

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Harvard University

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Massachusetts Institute of Technology

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New York University

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Notre Dam University

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Oklahoma University

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Pennsylvania State University

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Princeton University

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Stanford University

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University of California

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