[Solution] The minimum value of $n$ is 8.
First, we prove that each number in $s$ appears at least twice in the sequence $a_{1}, a_{2}, \cdots, a_{n}$.
In fact, if a number in $s$ appears only once in this sequence, since there are 3 subsets containing this number, but the number of adjacent pairs containing this number in the sequence is at most 2, it is impossible for all 3 subsets containing this number to appear as adjacent pairs in the sequence. This is a contradiction.

Therefore, $n \geqslant 8$.
On the other hand, the sequence $3,1,2,3,4,1,2,4$ satisfies the problem's conditions and has only 8 terms. Thus, the minimum value of $n$ is 8.
2・76 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 $n$.

