Question 25
$2n$ girls and $2n$ boys take part in a dancing party. It is known that for any two girls the number of the boys who have a dance with exactly one of these two girls is equal to $n$.
Prove that for any two boys the number of the girls who have a dance with exactly one of these two boys is equal to $n$ too.
Prove that for any two boys the number of the girls who have a dance with exactly one of these two boys is equal to $n$ too.