problem-solving techniques
Work backwards — AMC & AIME Problems
42 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Work backwards — 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: Working Backwards: Recursion, Induction, and Minimality.
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
- 2000 AMC 10 Problem 3
- 2002 AMC 10A Problem 6
- 2004 AMC 10B Problem 3
- 2009 AMC 10A Problem 8
- 2010 AMC 10A Problem 25
- 2011 AMC 10B Problem 2
- 2011 AMC 10B Problem 6
- 2012 AMC 10B Problem 11
- 2012 AMC 10B Problem 22
- 2013 AMC 10A Problem 21
- 2016 AMC 10A Problem 8
- 2017 AMC 10B Problem 1
- 2021 AMC 10B Spring Problem 9
- 2021 AMC 10A Fall Problem 2
- 2021 AMC 10A Fall Problem 23