There are $n$ kids. From each two at least one of them has sent an SMS to the other. For each kid $A$, among the kids on which $A$ has sent an SMS, exactly 10% of them have sent an SMS to $A$. Determine the number of possible three-digit values of $n$.
Problem
Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade
Tags: combinatorics