Problem 3
Twenty-one girls and twenty-one boys took part in a mathematical contest. Each contestant solved at most six problems. For each girl and each boy, at least one problem was solved by both of them. Prove that there was a problem solved by at least three girls and at least three boys.
Step 4 of 5: Bound labels with few boys
In plain words
Exchange girls and boys.
Detailed analysis
The same argument with girls and boys exchanged gives .