Doing this directly would be difficult, but we can use the matching condition to help. Construct a graph \(G\) with 13 vertices in the set \(A\text{,}\) each representing one of the 13 card values, and 13 vertices in the set \(B\text{,}\) each representing one of the 13 piles. Draw an edge between a vertex \(a \in A\) to a vertex \(b \in B\) if a card with value \(a\) is in the pile \(b\text{.}\) Notice that we are just looking for a matching of \(A\text{;}\) each value needs to be found in the piles exactly once.
in-context