11. $(2 n-1, n-2)=1$, when $3 \nmid n-2$; $=3$, when $3 \mid n-2$. When $(2 n-1, n-2)=1$, it belongs to at least 1 residue class modulo $n-2$; when $(2 n-1, n-2)=3$, it belongs to at least 3 residue classes modulo $n-2$. Generally, it belongs to at least $(K, m)$ residue classes modulo $m$.
11. Let $n>2$ be a given integer. How many residue classes modulo $n-2$ must a complete residue system modulo $2n-1$ at least belong to? Generally, for $K>m \geqslant 1$, how many residue classes modulo $m$ must a complete residue system modulo $K$ at least belong to?