Complementary counting — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Complementary counting — a combinatorics concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
1987 AMC 8 Problem 7 • 1998 AMC 8 Problem 21 • 2000 AMC 8 Problem 8 • 2003 AMC 8 Problem 18 • 2004 AMC 8 Problem 4 • 2005 AMC 8 Problem 21 • 2014 AMC 8 Problem 11 • 2016 AMC 8 Problem 17 • 2018 AMC 8 Problem 23 • 2020 AMC 8 Problem 10 • 2024 AMC 8 Problem 25
AMC 10
2004 AMC 10B Problem 11 • 2006 AMC 10A Problem 21 • 2007 AMC 10A Problem 12 • 2009 AMC 10A Problem 24 • 2010 AMC 10B Problem 22 • 2013 AMC 10A Problem 7 • 2016 AMC 10B Problem 12 • 2016 AMC 10B Problem 22 • 2017 AMC 10A Problem 23 • 2017 AMC 10B Problem 16 • 2018 AMC 10B Problem 5 • 2022 AMC 10A Problem 22 • 2022 AMC 10B Problem 18 • 2025 AMC 10B Problem 16
AMC 12
1959 AMC 12 Problem 46 • 1973 AMC 12 Problem 2 • 1990 AMC 12 Problem 16 • 2008 AMC 12A Problem 21 • 2008 AMC 12B Problem 22 • 2009 AMC 12B Problem 10 • 2011 AMC 12A Problem 22 • 2012 AMC 12A Problem 19 • 2012 AMC 12B Problem 13 • 2013 AMC 12A Problem 24 • 2013 AMC 12B Problem 21 • 2014 AMC 12B Problem 18 • 2016 AMC 12A Problem 11 • 2016 AMC 12B Problem 20 • 2018 AMC 12B Problem 5 • 2019 AMC 12B Problem 14 • 2021 AMC 12A Fall Problem 22 • 2022 AMC 12B Problem 12
AIME
1983 AIME Problem 7 • 1988 AIME Problem 1 • 1989 AIME Problem 2 • 1992 AIME Problem 15 • 1996 AIME Problem 6 • 1998 AIME Problem 2 • 1999 AIME Problem 7 • 2001 AIME II Problem 11 • 2004 AIME I Problem 3 • 2006 AIME II Problem 7 • 2008 AIME II Problem 12 • 2009 AIME II Problem 6 • 2010 AIME II Problem 8 • 2010 AIME II Problem 11 • 2011 AIME II Problem 12 • 2017 AIME I Problem 1 • 2017 AIME II Problem 11 • 2018 AIME II Problem 11 • 2022 AIME I Problem 6 • 2026 AIME I Problem 4 • 2026 AIME I Problem 7 • 2026 AIME II Problem 4