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JBMO Shortlist 2019 C4

Source:

September 12, 2020
combinatoricsJBMO Shortlist

Problem Statement

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