Exact cover
In the mathematical field of combinatorics, given a collection S {\displaystyle {\mathcal {S}}} of subsets of a set X {\displaystyle X} , an exact cover is a subcollection S ∗ {\displaystyle {\mathcal {S}}^{*}} of S {\displaystyle {\mathcal {S}}} such that each element in X {\displaystyle X} is contained in exactly one subset in S ∗ {\displaystyle {\mathcal {S}}^{*}} . One says that each element in X {\displaystyle X} is covered by exactly one subset in S ∗ {\displaystyle {\mathcal {S}}^{*}} .