Double counting — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Double 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 23 • 1999 AMC 8 Problem 11 • 2000 AMC 8 Problem 23 • 2005 AMC 8 Problem 14 • 2009 AMC 8 Problem 21 • 2020 AMC 8 Problem 16
AMC 10
2004 AMC 10A Problem 13 • 2005 AMC 10A Problem 17 • 2007 AMC 10A Problem 11 • 2023 AMC 10A Problem 6 • 2023 AMC 10A Problem 18
AMC 12
1959 AMC 12 Problem 50 • 1976 AMC 12 Problem 28 • 1989 AMC 12 Problem 30 • 1999 AMC 12 Problem 14 • 2001 AMC 12 Problem 14 • 2005 AMC 12A Problem 13 • 2009 AMC 12B Problem 20 • 2016 AMC 12A Problem 11 • 2017 AMC 12B Problem 25
AIME
1983 AIME Problem 13 • 1985 AIME Problem 14 • 1988 AIME Problem 10 • 1993 AIME Problem 10 • 1997 AIME Problem 10 • 2003 AIME I Problem 3 • 2009 AIME II Problem 12 • 2016 AIME II Problem 4 • 2017 AIME I Problem 7 • 2022 AIME I Problem 12 • 2023 AIME I Problem 3 • 2024 AIME I Problem 11 • 2024 AIME II Problem 1