problem-solving techniques
Invariant — AMC & AIME Problems
31 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Invariants and Monovariants in Dynamical Systems.
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
AMC 10
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