Difference between revisions of "2007 USAMO Problems/Problem 2"

 
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== Problem ==
 
== Problem ==
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A square grid on the Euclidean plane consists of all points <math>(m,n)</math>, where <math>m</math> and <math>n</math> 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?
  
 
== Solution ==
 
== Solution ==
  
== See also ==
 
 
{{USAMO newbox|year=2007|num-b=1|num-a=3}}
 
{{USAMO newbox|year=2007|num-b=1|num-a=3}}

Revision as of 16:57, 25 April 2007

Problem

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?

Solution

2007 USAMO (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6
All USAMO Problems and Solutions