Counting pairs — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Counting pairs — 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 10
2002 AMC 10B Problem 18 • 2004 AMC 10A Problem 13 • 2017 AMC 10A Problem 8 • 2021 AMC 10B Spring Problem 4 • 2021 AMC 10B Fall Problem 21 • 2024 AMC 10A Problem 6
AMC 12
1951 AMC 12 Problem 31 • 1969 AMC 12 Problem 19 • 1984 AMC 12 Problem 28 • 1989 AMC 12 Problem 27 • 2002 AMC 12B Problem 14 • 2011 AMC 12A Problem 9 • 2019 AMC 12B Problem 11
AIME
1994 AIME Problem 6 • 1995 AIME Problem 8 • 1996 AIME Problem 3 • 1996 AIME Problem 12 • 1997 AIME Problem 10 • 1998 AIME Problem 2 • 2001 AIME I Problem 10 • 2001 AIME II Problem 10 • 2002 AIME I Problem 5 • 2003 AIME I Problem 3 • 2004 AIME II Problem 10 • 2010 AIME II Problem 3 • 2010 AIME II Problem 4 • 2013 AIME I Problem 15 • 2015 AIME II Problem 5 • 2018 AIME I Problem 9 • 2019 AIME I Problem 2