Optimization — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses optimization — a problem-solving techniques 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
1985 AMC 8 Problem 24 · 1986 AMC 8 Problem 3 · 1986 AMC 8 Problem 14 · 1986 AMC 8 Problem 18 · 1987 AMC 8 Problem 6 · 1987 AMC 8 Problem 24 · 1988 AMC 8 Problem 14 · 1989 AMC 8 Problem 14 · 1989 AMC 8 Problem 20 · 1990 AMC 8 Problem 1 · 1990 AMC 8 Problem 7 · 1990 AMC 8 Problem 19 · 1991 AMC 8 Problem 8 · 1992 AMC 8 Problem 3 · 1993 AMC 8 Problem 25 · 1994 AMC 8 Problem 20 · 1996 AMC 8 Problem 6 · 1996 AMC 8 Problem 8 · 1997 AMC 8 Problem 2 · 1999 AMC 8 Problem 11 · 1999 AMC 8 Problem 15 · 2000 AMC 8 Problem 5 · 2000 AMC 8 Problem 7 · 2000 AMC 8 Problem 12 · 2001 AMC 8 Problem 4 · 2001 AMC 8 Problem 21 · 2002 AMC 8 Problem 1 · 2002 AMC 8 Problem 3 · 2003 AMC 8 Problem 8 · 2003 AMC 8 Problem 15 · 2005 AMC 8 Problem 5 · 2005 AMC 8 Problem 24 · 2006 AMC 8 Problem 22 · 2008 AMC 8 Problem 17 · 2010 AMC 8 Problem 7 · 2012 AMC 8 Problem 7 · 2012 AMC 8 Problem 16 · 2014 AMC 8 Problem 2 · 2014 AMC 8 Problem 19 · 2014 AMC 8 Problem 24 · 2018 AMC 8 Problem 14 · 2019 AMC 8 Problem 1 · 2019 AMC 8 Problem 7 · 2019 AMC 8 Problem 19 · 2020 AMC 8 Problem 8 · 2022 AMC 8 Problem 15 · 2023 AMC 8 Problem 6 · 2023 AMC 8 Problem 14 · 2023 AMC 8 Problem 18 · 2023 AMC 8 Problem 20 · 2024 AMC 8 Problem 15 · 2024 AMC 8 Problem 16 · 2024 AMC 8 Problem 19 · 2025 AMC 8 Problem 5 · 2025 AMC 8 Problem 12
AMC 10
2000 AMC 10 Problem 1 · 2000 AMC 10 Problem 20 · 2002 AMC 10A Problem 11 · 2002 AMC 10A Problem 18 · 2003 AMC 10B Problem 4 · 2003 AMC 10B Problem 14 · 2004 AMC 10A Problem 15 · 2004 AMC 10B Problem 5 · 2006 AMC 10A Problem 4 · 2006 AMC 10B Problem 5 · 2006 AMC 10B Problem 10 · 2007 AMC 10B Problem 24 · 2008 AMC 10B Problem 4 · 2010 AMC 10A Problem 16 · 2010 AMC 10A Problem 20 · 2010 AMC 10A Problem 21 · 2010 AMC 10B Problem 15 · 2011 AMC 10B Problem 3 · 2012 AMC 10A Problem 4 · 2012 AMC 10A Problem 10 · 2012 AMC 10A Problem 13 · 2013 AMC 10B Problem 5 · 2013 AMC 10B Problem 21 · 2014 AMC 10B Problem 18 · 2015 AMC 10B Problem 14 · 2016 AMC 10B Problem 16 · 2016 AMC 10B Problem 17 · 2017 AMC 10A Problem 2 · 2017 AMC 10A Problem 17 · 2018 AMC 10B Problem 14 · 2019 AMC 10A Problem 19 · 2019 AMC 10B Problem 12 · 2020 AMC 10A Problem 25 · 2021 AMC 10A Spring Problem 9 · 2021 AMC 10B Spring Problem 7 · 2021 AMC 10B Spring Problem 11 · 2021 AMC 10A Fall Problem 25 · 2021 AMC 10B Fall Problem 6 · 2022 AMC 10A Problem 25 · 2022 AMC 10B Problem 10 · 2023 AMC 10A Problem 13 · 2024 AMC 10A Problem 3 · 2024 AMC 10A Problem 4 · 2024 AMC 10A Problem 7 · 2024 AMC 10A Problem 15 · 2024 AMC 10A Problem 19 · 2024 AMC 10A Problem 20 · 2024 AMC 10B Problem 5 · 2024 AMC 10B Problem 6 · 2024 AMC 10B Problem 13 · 2024 AMC 10B Problem 16
AMC 12
1999 AMC 12 Problem 28 · 2000 AMC 12 Problem 1 · 2000 AMC 12 Problem 12 · 2002 AMC 12A Problem 9 · 2002 AMC 12A Problem 17 · 2003 AMC 12B Problem 3 · 2003 AMC 12B Problem 22 · 2004 AMC 12B Problem 2 · 2005 AMC 12B Problem 20 · 2006 AMC 12B Problem 10 · 2006 AMC 12B Problem 22 · 2007 AMC 12B Problem 20 · 2008 AMC 12A Problem 11 · 2008 AMC 12A Problem 24 · 2008 AMC 12B Problem 3 · 2008 AMC 12B Problem 19 · 2010 AMC 12A Problem 14 · 2010 AMC 12A Problem 22 · 2010 AMC 12B Problem 14 · 2010 AMC 12B Problem 22 · 2011 AMC 12A Problem 18 · 2011 AMC 12A Problem 24 · 2011 AMC 12A Problem 25 · 2011 AMC 12B Problem 7 · 2012 AMC 12A Problem 7 · 2012 AMC 12A Problem 8 · 2013 AMC 12A Problem 16 · 2014 AMC 12A Problem 20 · 2014 AMC 12B Problem 11 · 2015 AMC 12B Problem 12 · 2016 AMC 12B Problem 14 · 2017 AMC 12A Problem 1 · 2018 AMC 12A Problem 2 · 2018 AMC 12A Problem 24 · 2019 AMC 12B Problem 25 · 2020 AMC 12A Problem 23 · 2020 AMC 12B Problem 7 · 2020 AMC 12B Problem 22 · 2020 AMC 12B Problem 25 · 2021 AMC 12A Spring Problem 7 · 2021 AMC 12A Spring Problem 25 · 2021 AMC 12B Spring Problem 19 · 2021 AMC 12A Fall Problem 23 · 2022 AMC 12A Problem 22 · 2022 AMC 12B Problem 7 · 2022 AMC 12B Problem 9 · 2023 AMC 12A Problem 16 · 2023 AMC 12B Problem 11 · 2024 AMC 12A Problem 3 · 2024 AMC 12A Problem 6 · 2024 AMC 12A Problem 9 · 2024 AMC 12A Problem 12 · 2024 AMC 12B Problem 5 · 2024 AMC 12B Problem 13 · 2024 AMC 12B Problem 20 · 2025 AMC 12B Problem 22
AIME
1997 AIME Problem 15 · 2000 AIME I Problem 13 · 2004 AIME II Problem 3 · 2005 AIME I Problem 11 · 2006 AIME I Problem 15 · 2007 AIME II Problem 8 · 2008 AIME I Problem 12 · 2008 AIME I Problem 14 · 2008 AIME II Problem 3 · 2008 AIME II Problem 14 · 2009 AIME I Problem 14 · 2009 AIME I Problem 15 · 2009 AIME II Problem 15 · 2011 AIME I Problem 8 · 2011 AIME II Problem 8 · 2012 AIME II Problem 6 · 2013 AIME II Problem 10 · 2014 AIME I Problem 7 · 2016 AIME I Problem 9 · 2017 AIME I Problem 15 · 2017 AIME II Problem 5 · 2018 AIME I Problem 8 · 2018 AIME I Problem 13 · 2020 AIME II Problem 7 · 2022 AIME I Problem 7 · 2022 AIME II Problem 1 · 2022 AIME II Problem 6 · 2022 AIME II Problem 12 · 2022 AIME II Problem 14 · 2023 AIME I Problem 6 · 2024 AIME I Problem 7 · 2024 AIME I Problem 9 · 2024 AIME I Problem 15 · 2024 AIME II Problem 7 · 2024 AIME II Problem 12 · 2025 AIME I Problem 14 · 2025 AIME II Problem 8 · 2025 AIME II Problem 15 · 2026 AIME I Problem 11 · 2026 AIME II Problem 13