# Some Hard Problems on the 2016 AMC 8 are Exactly the Same as Previous Problems on the AMC 10/12 and the Other Competitions

Henry Wan, Ph.D.

We have developed a comprehensive, integrated, non-redundant, well-annotated database “CMP” consisting of competitive math problems, including all previous problems on the AMC 8/10/12, AIME, MATHCOUNTS, Math Kangaroo ContestMath Olympiads for Elementary and Middle Schools (MOEMS), ARML, HMMT, Math League, PUMaC, Stanford Math Tournament (SMT). The CPM is an invaluable “big data” system we use for our research and development, 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 those hard problems on the 2016 AMC 8, based on the database searching, we have found:

• 2016 AMC 8 Problem 21 is completely the same as 2001 AMC 10 Problem 23/2001 AMC 12 Problem 11
• 2016 AMC 8 Problem 24 is totally the same as the following problems:
• 2004 International Schools Mathematics Teachers Foundation (ISMTF) Junior Mathematics Competition – Team Event Problem 17
• 2005 BRITISH COLUMBIA COLLEGES Senior High School Mathematics Contest, Final Round, Part B (May 6, 2005) Problem 1.
• Click HERE to find this problem.
• 2008 Bermuda S2 US Grade 10 Mathematics Olympiad (May 4, 2008), Part B Problem 1
• Click HERE to find this problem.

In my AMC 10/12 Prep Class, I ever used Problem #23 on the 2001 AMC 10, as a typical example, to elegantly solve discrete probability problems on the AMC10/12, including the complementary probabilities. There were 23 middle schoolers to attend my AMC 10/12 Prep Class. When they attended the 2016 AMC 8, they already knew how to solve this problem and its answer. So they took one second to bubble the correct answer (B) and then got 1 point easily!

This year’s AMC 8 has a similar difficulty level as last year’s AMC 8; however, it was much more difficult than the AMC 8 of the years before 2015. Because the AMC 8 problems are getting harder, we must practice not only previous AMC 8 problems but also easy or medium difficulty level problems from previous AMC 10 to do well on the AMC 8.

Click HERE to see my detailed solutions of the hard problems on the 2016 AMC 8.

Click HERE find out more about Math Competitions!

Click HERE to find out more about SAT Prep!