Problem Set Workbook
Access the downloadable workbook for 2017 USAJMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2017 USAJMO Day 2 math contest by visiting Random Math USAJMO Day 2 2017 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2017 USAJMO Day 2 problems, please refer below:
Problem 4: Are there any triples of positive integers such that is a prime that properly divides the positive number
Solution:
Problem 5: (*) Let and be the circumcenter and the orthocenter of an acute triangle . Points and lie on side such that and . Ray intersects the circumcircle of triangle in point . Prove that .
Solution:
Problem 6: 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:
The problems on this page are the property of the MAA's American Mathematics Competitions