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Omni-MATH / An HMMT party has m MIT students and h Harvard students for some positive integers m and h, For every pair of people at the party, they are either friends or enemies. If every MIT …

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problem

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.
Plain-text mathematical notation (without MathML)
An HMMT party has m MIT students and h Harvard students for some positive integers m and h, 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.
Original LaTeX notation
An HMMT party has $m$ MIT students and $h$ Harvard students for some positive integers $m$ and $h$, 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.

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Source and history

task_id
2e123fb3-385e-5899-bdeb-c383223cb94e
task_key
test--2e123fb3-385e-5899-bdeb-c383223cb94e
task_revision_id
1
config / split
/ test

Official source

initial import