MathDB

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

and

G'

and two boys

B

and

B'

, such that each of

B

and

G

danced,

B'

and

G'

danced, but

B

and

G'

did not dance, and

B'

and

G

did not dance.

Problem Statement