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Love Triangle

Author: mathforces
Problem has been solved: 5 times

Русский язык | English Language

In a group of 2021 people, in each pair of people $A$ and $B$, either $A$ is in love with $B$ or $B$ is in love with $A$ (and love cannot be mutual). Let love triangle be a group of three people $X$, $Y$, and $Z$ such that $X$ is in love with $Y$, $Y$ is in love with $Z$, and $Z$ is in love with $X$. What is the largest possible number of love triangles in this group?

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