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 == | ||
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{{USAMO newbox|year=2007|num-b=1|num-a=3}} | {{USAMO newbox|year=2007|num-b=1|num-a=3}} | ||
Revision as of 17:57, 25 April 2007
Problem
A square grid on the Euclidean plane consists of all points 
, where 
and 
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 (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
