Difference between revisions of "1979 USAMO Problems/Problem 5"

(Problem)
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==Problem==
 
==Problem==
  
Let <math>A_1,A_2,...,A_{n+1}</math> be distinct subsets of <math>[n]</math> with <math>|A_1|=|A_2|=\cdots =|A_n|=3</math>.  Prove that <math>|A_i\cap A_j|=1</math> for some pair <math>\{i,j\}</math>
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Let <math>A_1,A_2,...,A_{n+1}</math> be distinct subsets of <math>[n]</math> with <math>|A_1|=|A_2|=\cdots =|A_n|=3</math>.  Prove that <math>|A_i\cap A_j|=1</math> for some pair <math>\{i,j\}</math>.
  
 
==Solution==
 
==Solution==
  
 
{{USAMO box|year=1979|num-b=4|after=Last Problem}}
 
{{USAMO box|year=1979|num-b=4|after=Last Problem}}

Revision as of 23:43, 11 April 2012

Problem

Let $A_1,A_2,...,A_{n+1}$ be distinct subsets of $[n]$ with $|A_1|=|A_2|=\cdots =|A_n|=3$. Prove that $|A_i\cap A_j|=1$ for some pair $\{i,j\}$.

Solution

1979 USAMO (ProblemsResources)
Preceded by
Problem 4
Followed by
Last Problem
1 2 3 4 5
All USAMO Problems and Solutions