Three, let $S=\{1,2,3,4\}, n$ terms of the sequence: $a_{1}$, $a_{2}, \cdots, a_{n}$ have the following property, for any non-empty subset $B$ of $S$ (the number of elements in $B$ is denoted as $|B|$), there are adjacent $|B|$ terms in the sequence that exactly form the set $B$. Find the minimum value of $n$.


Three, the minimum value of $n$ is 8.
First, prove that each number in $S$ appears at least 2 times in the sequence $a_{1}, a_{2}, \cdots, a_{n}$. This is because, if a number in $S$ appears only once in this sequence, since there are 3 two-element subsets containing this number, but in the sequence, the adjacent pairs containing this number can have at most two different combinations, it is impossible for all 3 two-element subsets containing this number to appear as adjacent pairs in the sequence.
Therefore, $n \geqslant 8$.
On the other hand, the 8-term sequence: $3,1,2,3,4,1,2,4$ satisfies the condition, so the required minimum value is 8.