Problem

Source: USAMO 2007

Tags: geometry, combinatorics, USAMO, combinatorial geometry, Soddy



A square grid on the Euclidean plane consists of all points $(m,n)$, where $m$ and $n$ are integers. Is it possible to cover all grid points by an infinite family of discs with non-overlapping interiors if each disc in the family has radius at least $5$?