Littlewood-Offord problem

[YaelDillies]

Let $x_1, \dots, x_n$ be vectors of norm at least $1$ a normed space. For $A \subseteq [n]$, set $x_A =
\sum_{i \in A} x_i$. Let $\McA \subseteq 2^{[n]}$ be such that
$$\forall A, B \in \McA, ||x_A - x_B|| < 1$$
Then $|\McA| \le {n \choose \lfloor\frac n2\rfloor}$.

This is Theorem 1.12 in the lecture notes and there is a start over at #21.