Consider a world with k men and h women. Man i's height is xi and woman j's height is yj for all i and j. Assume that no two individuals in this world have the same height. Also assume that both men and women prefer taller partners to shorter ones. Finally, both men and women prefer to be married to being single.

(a) How many stable matchings are possible in this world? Find them.

(b) Are there any unstable Pareto efficient matchings? Explain your answer.

(c) Suppose all women prefer shorter partners to taller ones. Is there more than one stable matching in this case?