Problem

Source: MOP 2006 Homework - Black Group

Tags: combinatorics unsolved, combinatorics



There are $b$ boys and $g$ girls, with $g \ge 2b-1$, at presence at a party. Each boy invites a girl for the first dance. Prove that this can be done in such a way that either a boy is dancing with a girl he knows or all the girls he knows are not dancing.