1. The minimum value of the function $f(x)=\sin 2022 x+|x-11|+|x-27|$ is
$|x-11|+|x-27| \geqslant|x-11+27-x|=16$, equality holds when $11 \leqslant x \leqslant 27$, and $\sin 2022 x \geqslant-1$, equality holds when $2022 x=\frac{3 \pi}{2}+2 k \pi \Rightarrow x=\frac{\pi}{1348}+\frac{k \pi}{1011}, k \in \mathbf{Z}$. Clearly, the intersection of the two is non-empty, so there exists $x$ such that the minimum value of the function $f(x)=\sin 2022 x+|x-11|+|x-27|$ is 15.