Invariant — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Invariant — a problem-solving techniques 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
1997 AMC 8 Problem 21 • 1998 AMC 8 Problem 25 • 2004 AMC 8 Problem 5 • 2007 AMC 8 Problem 22 • 2022 AMC 8 Problem 11
AMC 10
2000 AMC 10 Problem 17 • 2003 AMC 10B Problem 15 • 2013 AMC 10B Problem 17 • 2016 AMC 10A Problem 13 • 2024 AMC 10A Problem 6 • 2024 AMC 10B Problem 16
AMC 12
1956 AMC 12 Problem 6 • 1957 AMC 12 Problem 50 • 1991 AMC 12 Problem 28 • 1999 AMC 12 Problem 20 • 2004 AMC 12A Problem 7 • 2007 AMC 12B Problem 10 • 2013 AMC 12A Problem 6 • 2013 AMC 12B Problem 10 • 2013 AMC 12B Problem 16 • 2013 AMC 12B Problem 18 • 2015 AMC 12A Problem 13 • 2016 AMC 12A Problem 10 • 2019 AMC 12B Problem 19 • 2021 AMC 12B Spring Problem 22