MathDB

Several points are denoted on a white piece of paper. The distance between each two of the points is greater than

24

. A drop of ink was sprinkled over the paper covering an area smaller than

\pi

. Prove that there exists a vector

\overrightarrow v

with

\overrightarrow v<1

, such that after translating all of the points by

v

none of them is covered in ink.

Problem Statement