Problem Set Workbook
Access the downloadable workbook for 2018 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2018 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2018 Forum](https://forums.randommath.com/c/tournaments/MAA/2018-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2018 USAMO Day 2 problems, please refer below:
Problem 4: Let be a prime, and let be integers. Show that there exists an integer such that the numbers
produce at least distinct remainders upon division by .
Solution:
Problem 5: In convex cyclic quadrilateral , we know that lines and intersect at , lines and intersect at , and lines and intersect at . Suppose that the circumcircle of intersects line at and , and that the circumcircle of intersects line at and , where and are collinear in this order. Prove that if lines and intersect at , then .
Solution:
Problem 6: Let be the number of permutations of the numbers such that the ratios for are all distinct. Prove that is odd for all .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions