Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(New page: == Problem == I have an <math>n \times n</math> 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 t...)
 
m
Line 12: Line 12:
  
  
−
[[Category:Olympiad Algebra Problems]]
+
[[Category:Olympiad Combinatorics Problems]]

Revision as of 02:19, 21 December 2008

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Resources

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2002_USAMO_Problems/Problem_6&oldid=28675"