Modular arithmetic — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Modular arithmetic — a number theory 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).
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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
1985 AMC 8 Problem 20 • 1988 AMC 8 Problem 10 • 1992 AMC 8 Problem 15 • 1994 AMC 8 Problem 15 • 1995 AMC 8 Problem 15 • 1996 AMC 8 Problem 15 • 1996 AMC 8 Problem 20 • 1998 AMC 8 Problem 22 • 1998 AMC 8 Problem 24 • 1999 AMC 8 Problem 24 • 2000 AMC 8 Problem 20 • 2002 AMC 8 Problem 5 • 2003 AMC 8 Problem 23 • 2004 AMC 8 Problem 19 • 2005 AMC 8 Problem 20 • 2006 AMC 8 Problem 23 • 2007 AMC 8 Problem 18 • 2008 AMC 8 Problem 3 • 2011 AMC 8 Problem 22 • 2012 AMC 8 Problem 12 • 2012 AMC 8 Problem 15 • 2015 AMC 8 Problem 20 • 2015 AMC 8 Problem 24 • 2016 AMC 8 Problem 5 • 2017 AMC 8 Problem 12 • 2018 AMC 8 Problem 7 • 2018 AMC 8 Problem 13 • 2019 AMC 8 Problem 14 • 2023 AMC 8 Problem 14 • 2023 AMC 8 Problem 16 • 2023 AMC 8 Problem 18 • 2025 AMC 8 Problem 6 • 2025 AMC 8 Problem 13
AMC 10
2000 AMC 10 Problem 14 • 2000 AMC 10 Problem 17 • 2000 AMC 10 Problem 25 • 2002 AMC 10B Problem 8 • 2003 AMC 10A Problem 16 • 2003 AMC 10A Problem 25 • 2003 AMC 10B Problem 25 • 2006 AMC 10A Problem 20 • 2006 AMC 10B Problem 11 • 2006 AMC 10B Problem 16 • 2007 AMC 10A Problem 25 • 2007 AMC 10B Problem 9 • 2007 AMC 10B Problem 19 • 2008 AMC 10A Problem 24 • 2009 AMC 10B Problem 1 • 2009 AMC 10B Problem 13 • 2009 AMC 10B Problem 21 • 2010 AMC 10A Problem 10 • 2010 AMC 10A Problem 24 • 2010 AMC 10B Problem 5 • 2010 AMC 10B Problem 18 • 2012 AMC 10A Problem 12 • 2012 AMC 10B Problem 4 • 2013 AMC 10A Problem 19 • 2013 AMC 10B Problem 22 • 2013 AMC 10B Problem 25 • 2015 AMC 10B Problem 15 • 2016 AMC 10B Problem 4 • 2016 AMC 10B Problem 8 • 2017 AMC 10A Problem 13 • 2017 AMC 10A Problem 20 • 2017 AMC 10B Problem 23 • 2018 AMC 10B Problem 11 • 2018 AMC 10B Problem 13 • 2018 AMC 10B Problem 16 • 2020 AMC 10A Problem 24 • 2020 AMC 10B Problem 19 • 2020 AMC 10B Problem 22 • 2021 AMC 10A Fall Problem 12 • 2021 AMC 10B Fall Problem 22 • 2022 AMC 10A Problem 19 • 2022 AMC 10A Problem 25 • 2022 AMC 10B Problem 8 • 2022 AMC 10B Problem 17 • 2022 AMC 10B Problem 25 • 2023 AMC 10B Problem 8 • 2023 AMC 10B Problem 18 • 2024 AMC 10A Problem 10 • 2024 AMC 10A Problem 18 • 2024 AMC 10B Problem 4 • 2024 AMC 10B Problem 7 • 2024 AMC 10B Problem 24 • 2025 AMC 10A Problem 11 • 2025 AMC 10B Problem 8 • 2025 AMC 10B Problem 23
AMC 12
1951 AMC 12 Problem 37 • 1955 AMC 12 Problem 37 • 1957 AMC 12 Problem 32 • 1957 AMC 12 Problem 42 • 1958 AMC 12 Problem 32 • 1964 AMC 12 Problem 3 • 1964 AMC 12 Problem 16 • 1967 AMC 12 Problem 22 • 1967 AMC 12 Problem 24 • 1967 AMC 12 Problem 25 • 1969 AMC 12 Problem 24 • 1970 AMC 12 Problem 4 • 1971 AMC 12 Problem 11 • 1971 AMC 12 Problem 12 • 1971 AMC 12 Problem 25 • 1972 AMC 12 Problem 31 • 1973 AMC 12 Problem 18 • 1974 AMC 12 Problem 9 • 1976 AMC 12 Problem 15 • 1978 AMC 12 Problem 27 • 1979 AMC 12 Problem 22 • 1980 AMC 12 Problem 29 • 1982 AMC 12 Problem 26 • 1982 AMC 12 Problem 30 • 1985 AMC 12 Problem 9 • 1985 AMC 12 Problem 18 • 1985 AMC 12 Problem 23 • 1985 AMC 12 Problem 26 • 1988 AMC 12 Problem 12 • 1990 AMC 12 Problem 18 • 1990 AMC 12 Problem 19 • 1990 AMC 12 Problem 30 • 1992 AMC 12 Problem 23 • 1993 AMC 12 Problem 16 • 1995 AMC 12 Problem 15 • 1995 AMC 12 Problem 27 • 1998 AMC 12 Problem 30 • 1999 AMC 12 Problem 4 • 1999 AMC 12 Problem 25 • 2000 AMC 12 Problem 9 • 2000 AMC 12 Problem 18 • 2002 AMC 12B Problem 8 • 2002 AMC 12B Problem 10 • 2003 AMC 12A Problem 18 • 2003 AMC 12B Problem 18 • 2007 AMC 12A Problem 22 • 2008 AMC 12A Problem 17 • 2009 AMC 12A Problem 25 • 2010 AMC 12A Problem 23 • 2010 AMC 12B Problem 16 • 2011 AMC 12B Problem 25 • 2012 AMC 12A Problem 9 • 2012 AMC 12A Problem 17 • 2013 AMC 12A Problem 20 • 2013 AMC 12B Problem 18 • 2013 AMC 12B Problem 22 • 2013 AMC 12B Problem 23 • 2014 AMC 12B Problem 23 • 2015 AMC 12A Problem 22 • 2015 AMC 12B Problem 20 • 2016 AMC 12B Problem 5 • 2016 AMC 12B Problem 25 • 2017 AMC 12A Problem 18 • 2017 AMC 12B Problem 19 • 2019 AMC 12A Problem 21 • 2021 AMC 12B Spring Problem 20 • 2021 AMC 12A Fall Problem 10 • 2021 AMC 12A Fall Problem 25 • 2021 AMC 12B Fall Problem 25 • 2022 AMC 12A Problem 23 • 2022 AMC 12B Problem 15 • 2022 AMC 12B Problem 23 • 2023 AMC 12A Problem 24 • 2023 AMC 12B Problem 15 • 2024 AMC 12A Problem 11 • 2024 AMC 12B Problem 4 • 2025 AMC 12B Problem 5 • 2025 AMC 12B Problem 6 • 2025 AMC 12B Problem 19 • 2025 AMC 12B Problem 23
AIME
1983 AIME Problem 6 • 1984 AIME Problem 14 • 1985 AIME Problem 10 • 1986 AIME Problem 5 • 1988 AIME Problem 9 • 1992 AIME Problem 11 • 1993 AIME Problem 6 • 1993 AIME Problem 9 • 1994 AIME Problem 1 • 1994 AIME Problem 3 • 1995 AIME Problem 2 • 1995 AIME Problem 10 • 1996 AIME Problem 10 • 1999 AIME Problem 7 • 2001 AIME I Problem 11 • 2001 AIME II Problem 10 • 2001 AIME II Problem 14 • 2002 AIME I Problem 9 • 2002 AIME I Problem 14 • 2004 AIME I Problem 1 • 2007 AIME I Problem 5 • 2007 AIME II Problem 8 • 2007 AIME II Problem 13 • 2008 AIME II Problem 15 • 2009 AIME I Problem 7 • 2010 AIME I Problem 2 • 2011 AIME I Problem 5 • 2011 AIME I Problem 7 • 2011 AIME I Problem 11 • 2011 AIME II Problem 14 • 2012 AIME I Problem 10 • 2012 AIME I Problem 11 • 2012 AIME I Problem 15 • 2012 AIME II Problem 1 • 2012 AIME II Problem 12 • 2013 AIME I Problem 11 • 2013 AIME I Problem 15 • 2013 AIME II Problem 7 • 2013 AIME II Problem 14 • 2014 AIME I Problem 8 • 2014 AIME II Problem 4 • 2015 AIME II Problem 3 • 2016 AIME I Problem 12 • 2016 AIME II Problem 9 • 2016 AIME II Problem 11 • 2017 AIME I Problem 2 • 2017 AIME I Problem 9 • 2017 AIME II Problem 8 • 2018 AIME I Problem 11 • 2018 AIME I Problem 12 • 2018 AIME II Problem 2 • 2019 AIME II Problem 10 • 2019 AIME II Problem 14 • 2020 AIME II Problem 10 • 2021 AIME I Problem 14 • 2021 AIME II Problem 3 • 2022 AIME I Problem 2 • 2022 AIME I Problem 4 • 2022 AIME II Problem 8 • 2023 AIME I Problem 7 • 2023 AIME I Problem 10 • 2023 AIME I Problem 14 • 2023 AIME II Problem 10 • 2023 AIME II Problem 15 • 2024 AIME I Problem 3 • 2024 AIME I Problem 13 • 2024 AIME II Problem 7 • 2025 AIME I Problem 15 • 2025 AIME II Problem 2 • 2025 AIME II Problem 8 • 2026 AIME I Problem 8 • 2026 AIME I Problem 13 • 2026 AIME II Problem 3 • 2026 AIME II Problem 9 • 2026 AIME II Problem 15