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 1 of 5: Assume the contrary
In plain words
No problem has three solvers of each sex.
Detailed analysis
For each problem , let be its girl and boy solver sets. Assume or for every .