For example, let $3 x_{1}, x_{2}, \cdots, x_{n}$ be vectors (or complex numbers) with a modulus not less than 1. For any vector (or complex number) $x$, among the $2^{n}$ sums $x_{A}=\sum_{i \in A} x_{i}$, what is the maximum number that can be selected such that the modulus of their difference with $x$ is less than $\frac{1}{2}$?
If $\left|x_{A}-x\right|<\frac{1}{2},\left|x_{B}-x\right|<\frac{1}{2}$, then
$$
\left|x_{A}-x_{B}\right|<\frac{1}{2}+\frac{1}{2}=1 \text {. }
$$

Therefore, at most $C_{n}^{\left[\frac{n}{2}\right]}$ $x_{A}$ can be selected such that the modulus of the difference between $x_{A}$ and $x$ is less than $\frac{1}{2}$.