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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).
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
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
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