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cover all grid points by an infinite family of discs

Source: USAMO 2007

April 26, 2007

geometrycombinatoricsUSAMOcombinatorial geometrySoddy

Problem Statement

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

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