Bipartite Graphs and Matchings · Superchallenge problem

A bipartite graph has $X=\{1,2,3,4,5\}$ and $Y=\{a,b,c,d\}$, where every vertex of $X$ has degree EXACTLY $3$ (each missing exactly one of the $4$ vertices of $Y$, though different $X$-vertices may miss different ones). Over all such graphs, what is the SMALLEST possible value of the maximum matching?