Arrangements with restrictions — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Arrangements with restrictions — 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).
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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
1991 AMC 8 Problem 17 • 1994 AMC 8 Problem 24 • 2003 AMC 8 Problem 16 • 2004 AMC 8 Problem 2 • 2008 AMC 8 Problem 14 • 2011 AMC 8 Problem 23 • 2018 AMC 8 Problem 16 • 2020 AMC 8 Problem 10 • 2022 AMC 8 Problem 14 • 2026 AMC 8 Problem 17
AMC 10
2000 AMC 10 Problem 13 • 2006 AMC 10A Problem 18 • 2007 AMC 10B Problem 20 • 2008 AMC 10B Problem 21 • 2008 AMC 10B Problem 22 • 2010 AMC 10B Problem 23 • 2012 AMC 10B Problem 11 • 2012 AMC 10B Problem 22 • 2013 AMC 10A Problem 24 • 2014 AMC 10A Problem 4 • 2015 AMC 10A Problem 10 • 2015 AMC 10A Problem 22 • 2017 AMC 10A Problem 19 • 2018 AMC 10A Problem 4 • 2019 AMC 10B Problem 25 • 2021 AMC 10A Spring Problem 20 • 2021 AMC 10A Spring Problem 25 • 2021 AMC 10A Fall Problem 18 • 2021 AMC 10A Fall Problem 24 • 2022 AMC 10A Problem 9 • 2022 AMC 10A Problem 14 • 2022 AMC 10A Problem 24 • 2023 AMC 10A Problem 20 • 2024 AMC 10A Problem 20 • 2024 AMC 10B Problem 20
AMC 12
1989 AMC 12 Problem 9 • 2001 AMC 12 Problem 16 • 2005 AMC 12B Problem 25 • 2006 AMC 12B Problem 7 • 2008 AMC 12B Problem 22 • 2010 AMC 12B Problem 17 • 2012 AMC 12B Problem 8 • 2014 AMC 12A Problem 3 • 2017 AMC 12A Problem 14 • 2018 AMC 12A Problem 3 • 2022 AMC 12A Problem 10 • 2022 AMC 12A Problem 24 • 2025 AMC 12A Problem 23
AIME
1984 AIME Problem 11 • 1986 AIME Problem 13 • 1988 AIME Problem 15 • 1990 AIME Problem 8 • 1997 AIME Problem 8 • 2001 AIME I Problem 14 • 2003 AIME II Problem 3 • 2004 AIME I Problem 6 • 2005 AIME I Problem 5 • 2006 AIME II Problem 4 • 2007 AIME I Problem 10 • 2008 AIME I Problem 11 • 2008 AIME II Problem 12 • 2009 AIME I Problem 10 • 2011 AIME I Problem 12 • 2011 AIME II Problem 7 • 2012 AIME II Problem 3 • 2015 AIME II Problem 12 • 2016 AIME II Problem 13 • 2018 AIME I Problem 3 • 2019 AIME II Problem 5 • 2020 AIME I Problem 5 • 2020 AIME II Problem 9 • 2023 AIME II Problem 7 • 2024 AIME II Problem 9 • 2025 AIME I Problem 7 • 2025 AIME I Problem 10 • 2025 AIME II Problem 3 • 2025 AIME II Problem 10