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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).
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
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
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