Problem Set Workbook
Access the downloadable workbook for 2011 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2011 USAJMO Day 1 math contest by visiting Random Math USAJMO Day 1 2011 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2011 USAJMO Day 1 problems, please refer below:
Problem 1:
Find, with proof, all positive integers for which is a perfect square.
Solution:
Problem 2: Let be positive real numbers such that . Prove that
Solution:
Problem 3: For a point in the coordinate plane, let denote the line passing through with slope . Consider the set of triangles with vertices of the form , , such that the intersections of the lines form an equilateral triangle . Find the locus of the center of as ranges over all such triangles.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions