Individual Problems and Solutions
For problems and detailed solutions to each of the 2013 USAMO Day 2 problems, please refer below:
Problem 4: Find all real numbers satisfying
Solution:
Problem 5: Given positive integers and , prove that there is a positive integer such that the numbers and have the same number of occurrences of each non-zero digit when written in base ten.
Solution:
Problem 6: Let be a triangle. Find all points on segment satisfying the following property: If and are the intersections of line with the common external tangent lines of the circumcircles of triangles and , then
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions