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 2 of 5: Label the grid
In plain words
Every girl–boy pair has a shared problem.
Detailed analysis
Make a grid. In each cell choose one problem solved by the corresponding girl and boy.