2000 Putnam B6

Let $B$ be a set of more than $2^{n+1}/n$ distinct points with

coordinates

of the form $(\pm 1,\pm 1,\ldots,\pm 1)$ in $n$-dimensional space with

$n\geq 3$.

Show that there are three distinct points in $B$ which are the vertices of

an

equilateral triangle.

令 $B$ 为一组超过 $2^{n+1}/n$ 的不同点

坐标

形式为 $(\pm 1,\pm 1,\ldots,\pm 1)$ 在 $n$ 维空间中

$n\geq 3$。

表明 $B$ 中有三个不同的点，它们是

一个

等边三角形。