Problem Set Workbook
Access the downloadable workbook for 2016 USAMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2016 USAMO Day 1 math contest by visiting [Random Math USAMO Day 1 2016 Forum](https://forums.randommath.com/c/tournaments/MAA/2016-usamo-day 1)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2016 USAMO Day 1 problems, please refer below:
Problem 1: Let be a sequence of mutually distinct non-empty 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 .
Solution:
Problem 2: Prove that for any positive integer ,
is an integer.
Solution:
Problem 3: Let be an acute triangle, and let , and denote its -excenter, -excenter, and circumcenter, respectively. Points and are selected on such that and . Similarly, points and are selected on such that and .
Lines and meet at . Prove that and are perpendicular.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions