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 4: Let be the set of real numbers. Determine all functions such that
for all real numbers and .
Solution:
Problem 5: Let be integers greater than 2. Prove that there exists a positive integer and a finite sequence of positive integers such that , and is divisible by for each .
Solution:
Problem 6: I have an sheet of stamps, from which I've been asked to tear out blocks of three adjacent stamps in a single row or column. (I can only tear along the perforations separating adjacent stamps, and each block must come out of a sheet in one piece.) Let be the smallest number of blocks I can tear out and make it impossible to tear out any more blocks. Prove that there are real constants and such that
for all .
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions