Problem Set Workbook
Access the downloadable workbook for 2014 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2014 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2014 Forum](https://forums.randommath.com/c/tournaments/MAA/2014-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2014 USAMO Day 2 problems, please refer below:
Problem 4: Let be a positive integer. Two players and play a game on an infinite grid of regular hexagons. Initially all the grid cells are empty. Then the players alternately take turns with moving first. In his move, may choose two adjacent spaces in the grid which are empty and place a counter in both of them. In his move, may choose any counter on the board and remove it. If at any time there are consecutive grid cells in a line all of which contain a counter, wins. Find the minimum value of for which cannot win in a finite number of moves, or prove that no such minimum exists.
Solution:
Problem 5: Let be a triangle with orthocenter and let be the second intersection of the circumcircle of triangle with the internal bisector of the angle . Let be the circumcenter of triangle and the orthocenter of triangle . Prove that the length of segment is equal to the circumradius of triangle .
Solution:
Problem 6: Prove that there is a constant with the following property: If are positive integers such that for all , then
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions