Let $3 \leq k < n \in \mathbb{N}$. By $[n]^k$ we denote the collection of the subsets of $n = \{0,\ldots,n-1\}$ that have size $k$. We say that a hypergraph $H=(n,E)$ is $k$-*uniform* if $E\subseteq [n]^k$. Moreover, $H=(n, E)$ is *linear* if $|e_1\cap e_2| \leq 1$ for $e_1\neq e_2\in E$, and it is *maximal linear* if $E\subseteq E'\subseteq [n]^k$ and $E\neq E'$ imply that $(n, E')$ is no longer linear.

**Question.** Are there integers $k < n$ with $k\geq 3$ and maximal linear hypergraphs $H_i = (n, E_i)$ for $i = 1,2$ such that $|E_1| \neq |E_2|$? (If yes, it would also be interesting to know how big the difference of the edge sets can become in terms of $n$, but this information is not needed for acceptance of answer.)