Problem Set Workbook
Access the downloadable workbook for 2016 USAMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2016 USAMO Day 2 math contest by visiting [Random Math USAMO Day 2 2016 Forum](https://forums.randommath.com/c/tournaments/MAA/2016-usamo-day 2)
Individual Problems and Solutions
For problems and detailed solutions to each of the 2016 USAMO Day 2 problems, please refer below:
Problem 4: Find all functions such that for all real numbers and ,
Solution:
Problem 5: An equilateral pentagon is inscribed in triangle such that , and . Let be the intersection of and Denote by the angle bisector of .
Prove that is parallel to , where is the circumcenter of triangle , and is the incenter of triangle .
Solution:
Problem 6: Integers and are given, with . You play the following game against an evil wizard.
The wizard has cards; for each , there are two cards labeled . Initially, the wizard places all cards face down in a row, in unknown order.
You may repeatedly make moves of the following form: you point to any of the cards. The wizard then turns those cards face up. If any two of the cards match, the game is over and you win. Otherwise, you must look away, while the wizard arbitrarily permutes the chosen cards and then turns them back face-down. Then, it is your turn again.
We say this game is winnable if there exist some positive integer and some strategy that is guaranteed to win in at most moves, no matter how the wizard responds.
For which values of and is the game winnable?
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions