Problem Set Workbook
Access the downloadable workbook for 2015 USAMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2015 USAMO Day 1 math contest by visiting [Random Math USAMO Day 1 2015 Forum](https://forums.randommath.com/c/tournaments/MAA/2015-usamo-day 1)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2015 USAMO Day 1 problems, please refer below:
Problem 1: Solve in integers the equation
Solution:
Problem 2: Quadrilateral is inscribed in circle with and . Let be a variable point on segment . Line meets again at (other than ). Point lies on arc of such that is perpendicular to . Let denote the midpoint of chord . As varies on segment , show that moves along a circle.
Solution:
Problem 3: Let , where . Each of the subsets of is to be colored red or blue. (The subset itself is assigned a color and not its individual elements.) For any set , we then write for the number of subsets of that are blue.
Determine the number of colorings that satisfy the following condition: for any subsets and of ,
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions