There are six students, Harry, Ron, Hermione, Ginny, Draco, and Cho. This class requires them to

pair up and work on pair programming. Each has preferences over who they want to be paired

with. The preferences are:

Harry: Cho $>$ Ron $>$ Hermione $>$ Ginny $>$ Draco

Ron: Ginny $>$ Harry $>$ Hermione $>$ Cho $>$ Draco

Hermione: Ron $>$ Harry $>$ Ginny $>$ Cho $>$ Draco

Ginny: Harry $>$ Cho $>$ Hermione $>$ Ron $>$ Draco

Draco : Cho $>$ Ron $>$ Ginny $>$ Hermione $>$ Harry

Cho: Hermione $>$ Harry $>$ Ron $>$ Ginny $>$ Draco

Show that there is no stable matching. That means showing that no matter who you put together,

there will always be two potential partners who are not matched but prefer each other to the

current partner.