ÖMO 2018

On a circle $2018$ points are marked. Each of these points is labeled with an integer. Let each number be larger than the sum of the preceding two numbers in clockwise order. Determine the maximal number of positive integers that can occur in such a configuration of $2018$ integers.

(Proposed by Walther Janous)

Determine all digits $z$ such that for each integer $k \ge 1$ there exists an integer $n\ge 1$ with the property that the decimal representation of $n^9$ ends with at least $k$ digits $z$ .

(Proposed by Walther Janous)