Difference between revisions of "2016 USAMO Problems"
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Revision as of 10:20, 26 April 2016
Contents
Day 1
Problem 1
Let 
be a sequence of mutually distinct nonempty subsets of a set 
. Any two sets 
and 
are disjoint and their union is not the whole set , that is, 
and 
, for all 
. Find the smallest possible number of elements in .
Problem 2
This problem has not been edited in. If you know this problem, please help us out by adding it.
Problem 3
This problem has not been edited in. If you know this problem, please help us out by adding it.
Day 2
Problem 4
Find all functions 
such that for all real numbers 
and 
, ![\[(f(x)+xy)\cdot f(x-3y)+(f(y)+xy)\cdot f(3x-y)=(f(x+y))^2.\]](http://latex.artofproblemsolving.com/2/d/d/2ddcde1699356cbca5812e17244428064eb74546.png)
Problem 5
This problem has not been edited in. If you know this problem, please help us out by adding it.
Problem 6
This problem has not been edited in. If you know this problem, please help us out by adding it.
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
| 2016 USAMO (Problems • Resources) | ||
| Preceded by 2015 USAMO |
Followed by 2017 USAMO | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
