Exact cover

In mathematics, given a collection ${\displaystyle {\mathcal {S}}}$ of subsets of a set X, an exact cover is a subcollection ${\displaystyle {\mathcal {S}}^{*}}$ of ${\displaystyle {\mathcal {S}}}$ such that each element in X is contained in exactly one subset in ${\displaystyle {\mathcal {S}}^{*}}$. One says that each element in X is covered by exactly one subset in ${\displaystyle {\mathcal {S}}^{*}}$. An exact cover is a kind of cover.

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