Basic counting — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Basic counting — 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 7 • 1986 AMC 8 Problem 9 • 1998 AMC 8 Problem 11 • 2004 AMC 8 Problem 5 • 2005 AMC 8 Problem 14 • 2006 AMC 8 Problem 2 • 2009 AMC 8 Problem 9 • 2010 AMC 8 Problem 1 • 2011 AMC 8 Problem 3 • 2011 AMC 8 Problem 8 • 2013 AMC 8 Problem 22 • 2014 AMC 8 Problem 16 • 2016 AMC 8 Problem 18 • 2024 AMC 8 Problem 17 • 2026 AMC 8 Problem 2
AMC 10
2003 AMC 10B Problem 15 • 2004 AMC 10A Problem 6 • 2004 AMC 10A Problem 7 • 2004 AMC 10B Problem 1 • 2005 AMC 10A Problem 5 • 2008 AMC 10B Problem 1 • 2009 AMC 10B Problem 19 • 2012 AMC 10A Problem 14 • 2012 AMC 10B Problem 24 • 2015 AMC 10A Problem 18 • 2018 AMC 10B Problem 3 • 2023 AMC 10B Problem 11 • 2024 AMC 10B Problem 1
AMC 12
1952 AMC 12 Problem 31 • 1952 AMC 12 Problem 38 • 1959 AMC 12 Problem 46 • 1963 AMC 12 Problem 24 • 1965 AMC 12 Problem 29 • 1967 AMC 12 Problem 38 • 1970 AMC 12 Problem 31 • 1971 AMC 12 Problem 10 • 1971 AMC 12 Problem 24 • 1972 AMC 12 Problem 28 • 1975 AMC 12 Problem 17 • 1976 AMC 12 Problem 12 • 1977 AMC 12 Problem 20 • 1978 AMC 12 Problem 30 • 1981 AMC 12 Problem 22 • 1982 AMC 12 Problem 11 • 1985 AMC 12 Problem 20 • 2004 AMC 12A Problem 4 • 2005 AMC 12A Problem 4 • 2005 AMC 12A Problem 11 • 2006 AMC 12A Problem 24 • 2006 AMC 12B Problem 18 • 2010 AMC 12B Problem 15 • 2013 AMC 12A Problem 20 • 2015 AMC 12A Problem 24 • 2015 AMC 12B Problem 6 • 2017 AMC 12A Problem 5 • 2017 AMC 12A Problem 20 • 2018 AMC 12A Problem 15 • 2021 AMC 12B Spring Problem 2 • 2024 AMC 12B Problem 1