Problem Set Workbook
Access the downloadable workbook for 2018 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2018 USAJMO Day 1 math contest by visiting [Random Math USAJMO Day 1 2018 Forum](https://forums.randommath.com/c/tournaments/MAA/2018-usajmo-day 1)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2018 USAJMO Day 1 problems, please refer below:
Problem 1: For each positive integer , find the number of -digit positive integers that satisfy both of the following conditions:
Solution:
Problem 2: Let be positive real numbers such that . Prove that
Solution:
Problem 3: (*) Let be a quadrilateral inscribed in circle with . Let and be the reflections of over lines and , respectively, and let be the intersection of lines and . Suppose that the circumcircle of meets at and , and the circumcircle of meets at and . Show that .
(c) 2018, Mathematical Association of America.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions