Difference between revisions of "2007 USAMO Problems/Problem 3"
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | |||
| + | Let <math>S</math> be a set containing <math>n^2+n-1</math> elements, for some positive integer <math>n</math>. Suppose that the <math>n</math>-element subsets of <math>S</math> are partitioned into two classes. Prove that there are at least <math>n</math> pairwise disjoint sets in the same class. | ||
== Solution == | == Solution == | ||
| − | |||
{{USAMO newbox|year=2007|num-b=2|num-a=4}} | {{USAMO newbox|year=2007|num-b=2|num-a=4}} | ||
Revision as of 16:58, 25 April 2007
Problem
Let 
be a set containing 
elements, for some positive integer 
. Suppose that the -element subsets of are partitioned into two classes. Prove that there are at least pairwise disjoint sets in the same class.
Solution
| 2007 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
