Problem Set Workbook
Access the downloadable workbook for 2010 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2010 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2010 Forum](https://forums.randommath.com/c/tournaments/MAA/2010-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2010 USAMO Day 2 problems, please refer below:
Problem 4: Let be a triangle with . Points and lie on sides and , respectively, such that and . Segments and meet at . Determine whether or not it is possible for segments to all have integer lengths.
Solution:
Problem 5: Let where is an odd prime, and let
Prove that if for integers and , then is divisible by .
Solution:
Problem 6: A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer at most one of the pairs and is written on the blackboard. A student erases some of the 136 integers, subject to the condition that no two erased integers may add to 0 . The student then scores one point for each of the 68 pairs in which at least one integer is erased. Determine, with proof, the largest number of points that the student can guarantee to score regardless of which 68 pairs have been written on the board.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions