Problem Set Workbook
Access the downloadable workbook for 2011 USAJMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2011 USAJMO Day 2 math contest by visiting Random Math USAJMO Day 2 2011 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2011 USAJMO Day 2 problems, please refer below:
Problem 4: A word is defined as any finite string of letters. A word is a palindrome if it reads the same backwards as forwards. Let a sequence of words be defined as follows: , and for is the word formed by writing followed by . Prove that for any , the word formed by writing in succession is a palindrome.
Solution:
Problem 5: Points lie on circle and point lies outside the circle. The given points are such that (i) lines and are tangent to , (ii) are collinear, and (iii) . Prove that bisects .
Solution:
Problem 6: Consider the assertion that for each positive integer , the remainder upon dividing by is a power of 4 . Either prove the assertion or find (with proof) a counterexample.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions