Problem Set Workbook
Access the downloadable workbook for 2011 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2011 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2011 Forum](https://forums.randommath.com/c/tournaments/MAA/2011-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2011 USAMO Day 2 problems, please refer below:
Problem 4: Consider the assertion that for each positive integer , the remainder upon dividing by is a power of 4 . Either prove the assertion or find (with proof) a counterexample.
Solution:
Problem 5: Let be a given point inside quadrilateral . Points and are located within such that
Prove that if and only if .
Solution:
Problem 6: Let be a set with , meaning that has 225 elements. Suppose further that there are eleven subsets of such that for and for . Prove that , and give an example for which equality holds.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions