2

Part of 1964 Kurschak Competition

Problems(1)

dances of boys and girls at a party

Source: 1964 Hungary - Kürschák Competition p2

At a party every girl danced with at least one boy, but not with all of them. Similarly, every boy danced with at least one girl, but not with all of them. Show that there were two girls

G

G'

B

B'

, such that each of

B

G

B'

G'

B

G'

did not dance, and

B'

G