Problem Set Workbook
Access the downloadable workbook for 2002 USAMO problems here.
Discussion Forum
Engage in discussion about the 2002 USAMO math contest by visiting Random Math USAMO 2002 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2002 USAMO problems, please refer below:
Problem 1: Let be a set with elements, and let be an integer with . Prove that it is possible to color every subset of either black or white so that the following conditions hold:
a. the union of any two white subsets is white;
b. the union of any two black subsets is black;
c. there are exactly white subsets.
Solution:
Problem 2: Let be a triangle such that
where and denote its semiperimeter and its inradius, respectively. Prove that triangle is similar to a triangle whose side lengths are all positive integers with no common divisor and determine these integers.
Solution:
Problem 3: Prove that any monic polynomial (a polynomial with leading coefficient ) of degree with real coefficients is the average of two monic polynomials of degree with real roots.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions