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It is great that the AMS is able to conduct this competition which values and encourages mathematical talent. While sports are usually celebrated, it is wonderful that students interested in mathematics can also be encouraged. I sincerely hope that many more students gain the opportunity to participate in this competition.
For each year, there is a version without answers and a key with answers. The indicated year is the year that the national game, which takes place in January, was held. So, for example, the 2013 test was taken by students in the fall of 2012 to qualify for the national game in January 2013. Until 2013 there was only one round of testing; starting in 2014 we've had two rounds of tests. Note: Tests for regional games are the same level of difficulty as the Round One tests from 2014 on.
See previous qualifying tests: 2010, 2011, 2012, 2013, 2014 Round One, 2014 Round Two, 2015 Round One, 2015 Round Two, 2016 Round One, 2016 Round Two, 2017 Round One, 2017 Round Two, 2018 Round One, and 2018 Round Two.