Bounding to limit cases — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Bounding to limit cases — 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 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 10
2000 AMC 10 Problem 10 • 2000 AMC 10 Problem 11 • 2000 AMC 10 Problem 22 • 2001 AMC 10 Problem 14 • 2002 AMC 10A Problem 11 • 2002 AMC 10B Problem 7 • 2004 AMC 10B Problem 4 • 2004 AMC 10B Problem 13 • 2007 AMC 10A Problem 25 • 2009 AMC 10A Problem 2 • 2009 AMC 10A Problem 12 • 2010 AMC 10A Problem 8 • 2010 AMC 10A Problem 9 • 2010 AMC 10B Problem 12 • 2011 AMC 10A Problem 6 • 2017 AMC 10B Problem 6 • 2017 AMC 10B Problem 25 • 2018 AMC 10A Problem 14 • 2018 AMC 10A Problem 22 • 2019 AMC 10B Problem 24 • 2020 AMC 10B Problem 9 • 2021 AMC 10A Fall Problem 20 • 2021 AMC 10B Fall Problem 19 • 2023 AMC 10A Problem 4 • 2023 AMC 10B Problem 14 • 2023 AMC 10B Problem 22 • 2024 AMC 10A Problem 4 • 2024 AMC 10B Problem 5 • 2025 AMC 10B Problem 17
AMC 12
1958 AMC 12 Problem 32 • 1961 AMC 12 Problem 34 • 1963 AMC 12 Problem 34 • 1964 AMC 12 Problem 39 • 1965 AMC 12 Problem 21 • 1965 AMC 12 Problem 23 • 1965 AMC 12 Problem 40 • 1966 AMC 12 Problem 35 • 1967 AMC 12 Problem 23 • 1967 AMC 12 Problem 26 • 1971 AMC 12 Problem 27 • 1973 AMC 12 Problem 16 • 1974 AMC 12 Problem 28 • 1978 AMC 12 Problem 30 • 1981 AMC 12 Problem 28 • 1999 AMC 12 Problem 7 • 1999 AMC 12 Problem 9 • 1999 AMC 12 Problem 14 • 2000 AMC 12 Problem 13 • 2001 AMC 12 Problem 7 • 2002 AMC 12A Problem 9 • 2002 AMC 12B Problem 4 • 2002 AMC 12B Problem 24 • 2003 AMC 12B Problem 7 • 2004 AMC 12B Problem 11 • 2005 AMC 12A Problem 8 • 2005 AMC 12A Problem 21 • 2007 AMC 12A Problem 14 • 2007 AMC 12A Problem 22 • 2009 AMC 12A Problem 10 • 2009 AMC 12A Problem 12 • 2009 AMC 12A Problem 13 • 2010 AMC 12A Problem 5 • 2010 AMC 12A Problem 6 • 2010 AMC 12B Problem 13 • 2010 AMC 12B Problem 19 • 2011 AMC 12A Problem 7 • 2011 AMC 12A Problem 20 • 2011 AMC 12B Problem 7 • 2013 AMC 12A Problem 21 • 2013 AMC 12B Problem 15 • 2014 AMC 12A Problem 19 • 2014 AMC 12B Problem 13 • 2015 AMC 12A Problem 2 • 2017 AMC 12A Problem 11 • 2017 AMC 12B Problem 21 • 2018 AMC 12A Problem 21 • 2018 AMC 12B Problem 17 • 2019 AMC 12B Problem 6 • 2019 AMC 12B Problem 22 • 2020 AMC 12B Problem 8 • 2021 AMC 12B Spring Problem 21 • 2023 AMC 12B Problem 22 • 2024 AMC 12A Problem 3 • 2024 AMC 12A Problem 8 • 2024 AMC 12A Problem 21 • 2025 AMC 12B Problem 14
AIME
1986 AIME Problem 6 • 1987 AIME Problem 8 • 1990 AIME Problem 11 • 1998 AIME Problem 8 • 1998 AIME Problem 14 • 2001 AIME I Problem 8 • 2001 AIME II Problem 2 • 2003 AIME I Problem 1 • 2003 AIME I Problem 14 • 2007 AIME I Problem 14 • 2007 AIME II Problem 12 • 2007 AIME II Problem 14 • 2008 AIME I Problem 10 • 2010 AIME I Problem 5 • 2011 AIME II Problem 9 • 2013 AIME II Problem 6 • 2013 AIME II Problem 14 • 2016 AIME I Problem 12 • 2017 AIME I Problem 13 • 2018 AIME II Problem 3 • 2018 AIME II Problem 15 • 2020 AIME I Problem 3 • 2020 AIME I Problem 10 • 2021 AIME I Problem 15 • 2022 AIME I Problem 7 • 2025 AIME I Problem 1