we can find one pair of a boy and a girl
Source: Vietnam TST 2001 for the 42th IMO, problem 3
June 26, 2005
combinatorics unsolvedcombinatorics
Problem Statement
Some club has 42 members. It’s known that among 31 arbitrary club members, we can find one pair of a boy and a girl that they know each other. Show that from club members we can choose 12 pairs of knowing each other boys and girls.