Suppose that $\{D_n\}_{n\ge 1}$ is an finite sequence of disks in the plane whose total area is less than $1$. Prove that it is possible to rearrange the disks so that they are disjoint from each other and all contained inside a disk of area $4$.
Source:
Tags: combinatorics, 5th edition
Suppose that $\{D_n\}_{n\ge 1}$ is an finite sequence of disks in the plane whose total area is less than $1$. Prove that it is possible to rearrange the disks so that they are disjoint from each other and all contained inside a disk of area $4$.