Let $$A = \{1, 2, 3, 4\}$$ and $$R = \{(1,2), (2,3), (1,4)\}$$ be a relation on $$A$$. Let $$S$$ be the equivalence relation on $$A$$ such that $$R \subset S$$ and the number of elements in $$S$$ is $$n$$. Then, the minimum value of $$n$$ is _______

$$R=\{(1,2),(2,3),(1,4)\}$$. Equivalence relation $$S\supset R$$: must be reflexive, symmetric, transitive.

From $$(1,2)$$: need $$(2,1)$$. From $$(2,3)$$: need $$(3,2)$$. From $$(1,4)$$: need $$(4,1)$$.

Transitivity: $$(1,2),(2,3)\Rightarrow(1,3)$$, then $$(3,1)$$. $$(2,1),(1,4)\Rightarrow(2,4)$$, then $$(4,2)$$. $$(3,2),(2,4)\Rightarrow(3,4)$$, then $$(4,3)$$.

All elements {1,2,3,4} are in same equivalence class. So $$S=\{1,2,3,4\}^2$$, n=16.

The answer is $$\boxed{16}$$.