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HMMT November 2023 U30

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An HMMT party has mm MIT students and hh Harvard students for some positive integers mm and hh, For every pair of people at the party, they are either friends or enemies. If every MIT student has 16 MIT friends and 8 Harvard friends, and every Harvard student has 7 MIT enemies and 10 Harvard enemies, compute how many pairs of friends there are at the party.

Dataset text NuminaMath olympiads. Quoted with source.

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