Problem Set Workbook
Access the downloadable workbook for 2008 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2008 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2008 Forum](https://forums.randommath.com/c/tournaments/MAA/2008-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2008 USAMO Day 2 problems, please refer below:
Problem 4: Let be a convex polygon with sides, . Any set of diagonals of that do not intersect in the interior of the polygon determine a triangulation of into triangles. If is regular and there is a triangulation of consisting of only isosceles triangles, find all the possible values of .
Solution:
Problem 5: Three nonnegative real numbers are written on a blackboard. These numbers have the property that there exist integers , not all zero, satisfying . We are permitted to perform the following operation: find two numbers on the blackboard with , then erase and write in its place. Prove that after a finite number of such operations, we can end up with at least one 0 on the blackboard.
Solution:
Problem 6: At a certain mathematical conference, every pair of mathematicians are either friends or strangers. At mealtime, every participant eats in one of two large dining rooms. Each mathematician insists upon eating in a room which contains an even number of his or her friends. Prove that the number of ways that the mathematicians may be split between the two rooms is a power of two (i.e., is of the form for some positive integer ).
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions