Problem Set Workbook
Access the downloadable workbook for 2016 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2016 USAJMO Day 1 math contest by visiting Random Math USAJMO Day 1 2016 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2016 USAJMO Day 1 problems, please refer below:
Problem 1: The isosceles triangle , with , is inscribed in the circle . Let be a variable point on the arc that does not contain , and let and denote the incenters of triangles and , respectively.
Prove that as varies, the circumcircle of triangle passes through a fixed point.
Solution:
Problem 2: Prove that there exists a positive integer such that has six consecutive zeros in its decimal representation.
Solution:
Problem 3: 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:
The problems on this page are the property of the MAA's American Mathematics Competitions