Multiplication principle — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Multiplication principle — 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).
Filter by difficulty
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 22 • 1995 AMC 8 Problem 23 • 1999 AMC 8 Problem 15 • 2001 AMC 8 Problem 14 • 2003 AMC 8 Problem 16 • 2007 AMC 8 Problem 4 • 2009 AMC 8 Problem 22 • 2013 AMC 8 Problem 21 • 2015 AMC 8 Problem 4 • 2015 AMC 8 Problem 10 • 2015 AMC 8 Problem 11 • 2016 AMC 8 Problem 17 • 2017 AMC 8 Problem 15 • 2017 AMC 8 Problem 20 • 2018 AMC 8 Problem 19 • 2020 AMC 8 Problem 23 • 2023 AMC 8 Problem 23
AMC 10
2003 AMC 10B Problem 10 • 2003 AMC 10B Problem 16 • 2004 AMC 10A Problem 12 • 2005 AMC 10B Problem 12 • 2006 AMC 10A Problem 18 • 2007 AMC 10A Problem 12 • 2008 AMC 10A Problem 23 • 2010 AMC 10B Problem 22 • 2011 AMC 10A Problem 13 • 2012 AMC 10B Problem 11 • 2012 AMC 10B Problem 24 • 2012 AMC 10B Problem 25 • 2013 AMC 10B Problem 22 • 2018 AMC 10A Problem 20 • 2020 AMC 10A Problem 6 • 2020 AMC 10A Problem 18 • 2020 AMC 10A Problem 19 • 2022 AMC 10A Problem 9 • 2022 AMC 10A Problem 14 • 2022 AMC 10B Problem 3 • 2024 AMC 10A Problem 9 • 2025 AMC 10A Problem 12
AMC 12
1972 AMC 12 Problem 4 • 1985 AMC 12 Problem 11 • 1989 AMC 12 Problem 22 • 2006 AMC 12B Problem 7 • 2012 AMC 12B Problem 8 • 2012 AMC 12B Problem 16 • 2012 AMC 12B Problem 22 • 2013 AMC 12A Problem 15 • 2013 AMC 12B Problem 12 • 2014 AMC 12A Problem 13 • 2018 AMC 12B Problem 15 • 2020 AMC 12A Problem 4 • 2022 AMC 12A Problem 7 • 2022 AMC 12A Problem 10 • 2022 AMC 12B Problem 17 • 2023 AMC 12A Problem 24 • 2024 AMC 12B Problem 16 • 2025 AMC 12B Problem 13
AIME
1983 AIME Problem 10 • 1986 AIME Problem 13 • 1987 AIME Problem 1 • 1987 AIME Problem 7 • 1988 AIME Problem 15 • 1993 AIME Problem 8 • 1994 AIME Problem 5 • 2002 AIME II Problem 9 • 2003 AIME II Problem 3 • 2004 AIME II Problem 4 • 2005 AIME I Problem 5 • 2007 AIME I Problem 6 • 2007 AIME II Problem 1 • 2007 AIME II Problem 6 • 2007 AIME II Problem 13 • 2009 AIME I Problem 9 • 2010 AIME I Problem 7 • 2011 AIME I Problem 5 • 2013 AIME I Problem 2 • 2013 AIME II Problem 9 • 2016 AIME I Problem 3 • 2016 AIME II Problem 8 • 2019 AIME I Problem 4 • 2023 AIME II Problem 7 • 2024 AIME II Problem 9 • 2025 AIME I Problem 10 • 2025 AIME II Problem 3 • 2026 AIME II Problem 2