2016 USAMO Problems
Contents
[hide]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 ,
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 |