I am reading the Wikipedia article entitled Hall's marriage theorem. It states we can use the theorem to prove the following:
"Take a standard deck of cards, and deal them out into 13 piles of 4 cards each. Then, using the marriage theorem, we can show that it is always possible to select exactly 1 card from each pile, such that the 13 selected cards contain exactly one card of each rank (Ace, 2, 3, ..., Queen, King)."
The article doesn't say HOW Hall's theorem can be used to prove this.
I think we could create a bipartite graph with one partite set consisting of each of the 13 ranks and the other partite set consisting of the 13 piles. An edge joins a rank to a pile if that rank is in the pile. Each rank would be joined to at least one pile and at most 4 piles. This is as far as I have gotten.