Problem Set Workbook
Access the downloadable workbook for 2010 USAJMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2010 USAJMO Day 2 math contest by visiting Random Math USAJMO Day 2 2010 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2010 USAJMO Day 2 problems, please refer below:
Problem 4: A triangle is called a parabolic triangle if its vertices lie on a parabola . Prove that for every nonnegative integer , there is an odd number and a parabolic triangle with vertices at three distinct points with integer coordinates with area .
Solution:
Problem 5: Two permutations and of the numbers are said to intersect if for some value of in the range . Show that there exist 1006 permutations of the numbers such that any other such permutation is guaranteed to intersect at least one of these 1006 permutations.
Solution:
Problem 6: 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:
The problems on this page are the property of the MAA's American Mathematics Competitions