Problem Set Workbook
Access the downloadable workbook for 2012 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2012 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2012 Forum](https://forums.randommath.com/c/tournaments/MAA/2012-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2012 USAMO Day 2 problems, please refer below:
Problem 4: Find all functions (where is the set of positive integers) such that ! for all positive integers and such that divides for all distinct positive integers .
Solution:
Problem 5: Let be a point in the plane of , and a line passing through . Let be the points where the reflections of lines with respect to intersect lines , respectively. Prove that are collinear.
Solution:
Problem 6: For integer , let be real numbers satisfying
For each subset , define
(If is the empty set, then .)
Prove that for any positive number , the number of sets satisfying is at most . For what choices of does equality hold?
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions