Question 162
Twenty-one girls and twenty-one boys took part in a mathematical competition. It turned out that
a. each contestant solved at most six problems, and
b. for each pair of a girl and a boy, there was at least one problem that was solved by both the girl and the boy.
Prove that there is a problem that was solved by at least three girls and at least three boys.
a. each contestant solved at most six problems, and
b. for each pair of a girl and a boy, there was at least one problem that was solved by both the girl and the boy.
Prove that there is a problem that was solved by at least three girls and at least three boys.