JBMO-SL 2019 C4

Combinatorics
Answer

We have a group of $n$ kids. For each pair of kids, at least one has sent a message to the other one. For each kid $A$ , among the kids to whom $A$ has sent a message, exactly $25 \%$ have sent a message to $A$ . How many possible two-digit values of $n$ are there?

Dataset text NuminaMath olympiads. Quoted with source.

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