Recursion — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Recursion — a algebra 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).

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AMC 8

1990 AMC 8 Problem 21 1998 AMC 8 Problem 22 2009 AMC 8 Problem 5 2023 AMC 8 Problem 22

AMC 12

1950 AMC 12 Problem 42 1951 AMC 12 Problem 42 1958 AMC 12 Problem 40 1964 AMC 12 Problem 31 1966 AMC 12 Problem 25 1969 AMC 12 Problem 32 1970 AMC 12 Problem 16 1971 AMC 12 Problem 30 1975 AMC 12 Problem 15 1976 AMC 12 Problem 25 1977 AMC 12 Problem 13 1978 AMC 12 Problem 28 1979 AMC 12 Problem 26 1982 AMC 12 Problem 30 1984 AMC 12 Problem 12 1985 AMC 12 Problem 27 1989 AMC 12 Problem 10 1999 AMC 12 Problem 20 2001 AMC 12 Problem 25 2004 AMC 12A Problem 17 2004 AMC 12B Problem 12 2005 AMC 12A Problem 20 2005 AMC 12B Problem 10 2005 AMC 12B Problem 22 2006 AMC 12A Problem 23 2008 AMC 12A Problem 17 2008 AMC 12B Problem 24 2009 AMC 12A Problem 24 2009 AMC 12A Problem 25 2009 AMC 12B Problem 11 2009 AMC 12B Problem 21 2011 AMC 12A Problem 21 2011 AMC 12B Problem 17 2011 AMC 12B Problem 22 2012 AMC 12B Problem 24 2013 AMC 12A Problem 7 2014 AMC 12A Problem 24 2015 AMC 12B Problem 20 2016 AMC 12B Problem 21 2016 AMC 12B Problem 25 2017 AMC 12A Problem 7 2018 AMC 12B Problem 18 2019 AMC 12A Problem 9 2019 AMC 12A Problem 17 2019 AMC 12A Problem 25 2019 AMC 12B Problem 22 2021 AMC 12A Spring Problem 8 2021 AMC 12A Fall Problem 20 2021 AMC 12B Fall Problem 18 2022 AMC 12A Problem 16 2023 AMC 12A Problem 17 2023 AMC 12A Problem 20 2023 AMC 12A Problem 22 2024 AMC 12A Problem 21

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absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencearithmetico-geometric seriesbinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex numbercustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctionfunctional equationgeometric sequenceinequalitylinear equationlogarithmmatrixmixtureNewton’s Sumspartial fractionspolynomialquadraticradicalrational equationrationalizing denominatorroots of unitySimon’s Favorite Factoring Trickslopesubstitutionsum and difference of cubessum of first n cubessum of first n odd numberssum of first n squaressummationsymmetry (algebra)system of equationstelescopingVieta’s Formulaszero product property