Problem Set Workbook
Access the downloadable workbook for 2003 USAMO problems here.
Discussion Forum
Engage in discussion about the 2003 USAMO math contest by visiting Random Math USAMO 2003 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2003 USAMO problems, please refer below:
Problem 4: Let be a triangle. A circle passing through and intersects segments and at and , respectively. Lines and intersect at while lines and intersect at . Prove that if and only if .
Solution:
Problem 5: Let be positive real numbers. Prove that
Solution:
Problem 6: A positive integer is written at each vertex of a regular hexagon so that the sum of all numbers written is . Bert makes a sequence of moves of the following form: Bert picks a vertex and replaces the number written there by the absolute value of the difference between the numbers written at the two neighboring vertices. Prove that Bert can always make a sequence of moves ending at the position with all six numbers equal to zero.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions