Problem Set Workbook
Access the downloadable workbook for 2006 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2006 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2006 Forum](https://forums.randommath.com/c/tournaments/MAA/2006-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2006 USAMO Day 2 problems, please refer below:
Problem 4: Find all positive integers such that there are positive rational numbers satisfying .
Solution:
Problem 5: A mathematical frog jumps along the number line. The frog starts at 1 , and jumps according to the following rule: if the frog is at integer , then it can jump either to or to where is the largest power of 2 that is a factor of . Show that if is a positive integer and is a nonnegative integer, then the minimum number of jumps needed to reach is greater than the minimum number of jumps needed to reach .
Solution:
Problem 6: Let be a quadrilateral, and let and be points on sides and , respectively, such that . Ray meets rays and at and , respectively. Prove that the circumcircles of triangles , and pass through a common point.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions