Difference between revisions of "2002 USAMO Problems/Problem 6"

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== Resources ==
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== See also ==
 
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{{USAMO newbox|year=2002|num-b=5|after=Last question}}
* [[2002 USAMO Problems]]
 
* [http://www.mathlinks.ro/viewtopic.php?p=337852#337852 Discussion on AoPS/MathLinks]
 
  
  
 
[[Category:Olympiad Combinatorics Problems]]
 
[[Category:Olympiad Combinatorics Problems]]

Revision as of 21:49, 6 April 2013

Problem

I have an $n \times n$ sheet of stamps, from which I've been asked to tear out blocks of three adjacent stamps in a single row or column. (I can only tear along the perforations separating adjacent stamps, and each block must come out of the sheet in one piece.) Let $b(n)$ be the smallest number of blocks I can tear out and make it impossible to tear out any more blocks. Prove that there are real constants $c$ and $d$ such that

$\dfrac{1}{7} n^2 - cn \leq b(n) \leq \dfrac{1}{5} n^2 + dn$

for all $n > 0$.

Solutions

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See also

2002 USAMO (ProblemsResources)
Preceded by
Problem 5
Followed by
Last question
1 2 3 4 5 6
All USAMO Problems and Solutions