# Some Problems on the 2016 AMC 10/12 are Exactly the Same as Previous AMC/ARML Problems

Henry Wan, Ph.D.

We have developed a comprehensive, integrated, non-redundant, well-annotated database “CMP” consisting of competitive math problems, including all previous AMC 10/12 problems, AIME problems, ARML problems, HMMT problems, Math League problems, PUMaC problems, Stanford Math Tournament (SMT) problems. The CPM is an invaluable “big data” system we use for our research, and is a golden resource for our students, who are the ultimate beneficiaries.

We have also devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we can align query math problems against those present in the target database “CPM,” and then find those similar problems in the CMP database.

For the 2016 AMC 10/12A and 10/12B problems, based on the database searching, we have found:

• 2016 AMC 10A Problem 15 is similar to 2002 AMC 10A #5.
• 2016 AMC 10A Problem 18 is similar to 2007 AMC 10A #11.
• 2016 AMC 10B Problem 21 is completely the same as 2014 ARML Team Round Problem 8
• 2016 AMC 10B Problem 21 is similar to the following problems:
• 2008 AMC 12A Problem 14
• 1987 AIME Problem 4
• 2014 University of Maryland High School Mathematics Competition Problem 16

Click HERE to see my complete detailed article on the similarities between the 2016 AMC 10/12 problems and previous math competition problems.

In my AMC 10/12 Prep Class on Feb. 14, 2016, I used Problem 8 in the 2014 ARML Team Round and the 2008 AMC 12A Problem 14, as two typical examples, to illustrate how to efficiently compute the area of the region defined by inequalities or bounded by a simple closed curve. Thus, when my students attended the 2016 AMC 10B, they already knew how to solve this exact problem and its answer. So they took one second to bubble the correct answer (B) and then got 6 points easily!