4

Part of 2024 Czech and Slovak Olympiad III A

Problems(1)

10 boys and 10 girls at the party

Source: 2024 Czech and Slovak Olympiad III A p4

10

10

girls at the party. Every boy likes a different 'positive' number of girls. Every girl likes a different positive number of boys. Define the largest non-negative integer

n

such that it is always possible to form at least

n

disjoint pairs in which both like the other.