Problem Set Workbook
Access the downloadable workbook for 2013 USAJMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2013 USAJMO Day 2 math contest by visiting Random Math USAJMO Day 2 2013 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2013 USAJMO Day 2 problems, please refer below:
Problem 4: Let be the number of ways to write as a sum of powers of 2 , where we keep track of the order of the summation. For example, because 4 can be written as , , and . Find the smallest greater than 2013 for which is odd.
Solution:
Problem 5: Quadrilateral is inscribed in the semicircle with diameter . Segments and meet at . Point is the foot of the perpendicular from to line . Point lies on such that line is perpendicular to line . Let be the intersection of segments and . Prove that
Solution:
Problem 6: Find all real numbers satisfying
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions