Problem Set Workbook
Access the downloadable workbook for 2017 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2017 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2017 Forum](https://forums.randommath.com/c/tournaments/MAA/2017-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2017 USAMO Day 2 problems, please refer below:
Problem 4: Let be distinct points on the unit circle other than . Each point is colored either red or blue, with exactly of them red and of them blue. Let be any ordering of the red points. Let be the nearest blue point to traveling counterclockwise around the circle starting from . Then let be the nearest of the remaining blue points to traveling counterclockwise around the circle from , and so on, until we have labeled all of the blue points . Show that the number of counterclockwise arcs of the form that contain the point is independent of the way we chose the ordering of the red points.
Solution:
Problem 5: Let denote the set of all integers. Find all real numbers such that there exists a labeling of the lattice points with positive integers for which:
Solution:
Problem 6: Find the minimum possible value of
given that are nonnegative real numbers such that .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions