Difference between revisions of "1979 USAMO Problems/Problem 5"
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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> | + | 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 
be distinct subsets of ![$[n]$](http://latex.artofproblemsolving.com/0/d/e/0deff9086fd7840ef23860f5bc924f1d4d2d2310.png)
with 
. Prove that 
for some pair 
.
Solution
| 1979 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
