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