Counting integers in a range — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Counting integers in a range — 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
1986 AMC 8 Problem 7 • 2000 AMC 8 Problem 3 • 2003 AMC 8 Problem 19 • 2005 AMC 8 Problem 18 • 2008 AMC 8 Problem 22 • 2018 AMC 8 Problem 21 • 2018 AMC 8 Problem 25 • 2022 AMC 8 Problem 13
AMC 10
2001 AMC 10 Problem 25 • 2003 AMC 10A Problem 15 • 2003 AMC 10A Problem 20 • 2003 AMC 10A Problem 25 • 2004 AMC 10B Problem 1 • 2005 AMC 10A Problem 13 • 2005 AMC 10A Problem 22 • 2005 AMC 10B Problem 13 • 2006 AMC 10A Problem 10 • 2006 AMC 10A Problem 19 • 2013 AMC 10A Problem 17 • 2013 AMC 10B Problem 4 • 2014 AMC 10A Problem 25 • 2014 AMC 10B Problem 20 • 2015 AMC 10A Problem 13 • 2017 AMC 10A Problem 10 • 2018 AMC 10A Problem 7 • 2018 AMC 10A Problem 16 • 2018 AMC 10B Problem 13 • 2018 AMC 10B Problem 25 • 2020 AMC 10A Problem 11 • 2020 AMC 10A Problem 17 • 2021 AMC 10B Spring Problem 1 • 2023 AMC 10A Problem 12 • 2023 AMC 10B Problem 9 • 2024 AMC 10A Problem 18 • 2024 AMC 10B Problem 3
AMC 12
1957 AMC 12 Problem 16 • 1957 AMC 12 Problem 43 • 1963 AMC 12 Problem 31 • 1964 AMC 12 Problem 16 • 1966 AMC 12 Problem 29 • 1967 AMC 12 Problem 24 • 1968 AMC 12 Problem 19 • 1975 AMC 12 Problem 18 • 1978 AMC 12 Problem 19 • 1983 AMC 12 Problem 16 • 1989 AMC 12 Problem 8 • 1989 AMC 12 Problem 11 • 1989 AMC 12 Problem 17 • 1990 AMC 12 Problem 19 • 1999 AMC 12 Problem 11 • 2001 AMC 12 Problem 12 • 2002 AMC 12B Problem 10 • 2003 AMC 12B Problem 23 • 2004 AMC 12A Problem 3 • 2004 AMC 12B Problem 23 • 2005 AMC 12A Problem 18 • 2006 AMC 12A Problem 10 • 2008 AMC 12B Problem 1 • 2010 AMC 12B Problem 25 • 2013 AMC 12B Problem 3 • 2015 AMC 12A Problem 19 • 2017 AMC 12A Problem 6 • 2019 AMC 12B Problem 9 • 2020 AMC 12A Problem 8 • 2022 AMC 12B Problem 6 • 2024 AMC 12A Problem 11 • 2024 AMC 12B Problem 1 • 2024 AMC 12B Problem 3 • 2025 AMC 12B Problem 19
AIME
1984 AIME Problem 10 • 1984 AIME Problem 12 • 1985 AIME Problem 10 • 1990 AIME Problem 1 • 1991 AIME Problem 6 • 1993 AIME Problem 4 • 1994 AIME Problem 1 • 1994 AIME Problem 11 • 1995 AIME Problem 13 • 1996 AIME Problem 2 • 1997 AIME Problem 5 • 2002 AIME II Problem 8 • 2005 AIME II Problem 5 • 2006 AIME I Problem 2 • 2006 AIME I Problem 8 • 2007 AIME I Problem 11 • 2007 AIME II Problem 7 • 2008 AIME I Problem 7 • 2009 AIME I Problem 6 • 2009 AIME II Problem 11 • 2010 AIME I Problem 5 • 2012 AIME II Problem 10 • 2025 AIME I Problem 4 • 2026 AIME II Problem 3