Dutch Mathematical Olympiad

An integer $n$ is a combi number if each pair of distinct digits from the set of all possible digits $0$ to $9$ appear at least once in the number as neighbouring digits. For example, in a combi number the digits $3$ and $5$ have to appear somewhere next to each other. It does not matter whether they appear in the order $35$ or $53$. We take the convention that a combi number never starts with the digit $0$. What is the smallest possible number of digits of a combi number?