Question 86
$2n$ girls and $2n$ boys take part in a dancing party. It is known that Bob has a dance with every girl, and Ann has a dance with every boy. Moreover, 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
a) any girl, except for Ann, has a dance with exactly $n$ boys;
b) any boy, except for Bob, has a dance with exactly $n$ girls.
Prove that
a) any girl, except for Ann, has a dance with exactly $n$ boys;
b) any boy, except for Bob, has a dance with exactly $n$ girls.