Problem Set Workbook
Access the downloadable workbook for 2014 USAJMO Day 1 problems here.
Discussion Forum
Engage in discussion about the 2014 USAJMO Day 1 math contest by visiting Random Math USAJMO Day 1 2014 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2014 USAJMO Day 1 problems, please refer below:
Problem 1: Let be real numbers greater than or equal to 1 . Prove that
Solution:
Problem 2: Let be a non-equilateral, acute triangle with , and let and denote the circumcenter and orthocenter of , respectively.
(1) Prove that line intersects both segments and .
(2) Line intersects segments and at and , respectively. Denote by and the respective areas of triangle and quadrilateral . Determine the range of possible values for .
Solution:
Problem 3: Let be the set of integers. Find all functions such that
for all with .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions