Task 2. Using each of the digits from 0 to 9 exactly once, write down 5 non-zero numbers such that each divides the previous one. $\quad[6$ points] (A.V. Shapovalov)
Answer. For example, $1,2,4,8,975360$.

Comment. It is easier to check divisibility when most numbers are written with 1-2 digits, and for this, most of the quotients should be quite small ( $2,3, \ldots$ ). Start with the smallest sequence: $1,2,4,8$. Whether the remaining number is divisible by 8 depends only on its last three digits. Therefore, it is easy to get a number from the remaining digits that is divisible by 8 - especially if you place 0 at the last position.

There are many other solutions: for example, $9,18,36,72,504$.