A property of Kolmogorov random strings
Suppose that $x = x_1 \cdots x_n$, where $|x_i| = k$, and there exists some $z \in \{0,1\}^k$ such that $x_i \neq z$ for all $i$. We can encode $x$ by first listing $z$, and then encoding each $x_i$ using $\log_2 (2^k-1)$ fractional bits. The program also needs to know $n$. This shows that
$$
K(x) \leq \log_2 (2^k-1) \cdot n + C_k + O(\log n),
$$
where $C_k$ is a constant that depends only on $k$. In particular, if $n$ is large enough that the upper bound will be less than $nk$.