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HMMT 2014 T3

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There are nn girls G1,…,GnG_{1}, \ldots, G_{n} and nn boys B1,…,BnB_{1}, \ldots, B_{n}. A pair (Gi,Bj)\left(G_{i}, B_{j}\right) is called suitable if and only if girl GiG_{i} is willing to marry boy BjB_{j}. Given that there is exactly one way to pair each girl with a distinct boy that she is willing to marry, what is the maximal possible number of suitable pairs?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{n(n+1)}{2}

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