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Power of 2 — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Power of 2 — a number theory 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.

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AMC 8

2013 AMC 8 Problem 9 • 2016 AMC 8 Problem 15

AMC 10

2009 AMC 10B Problem 6 • 2014 AMC 10B Problem 17 • 2021 AMC 10B Fall Problem 5 • 2022 AMC 10B Problem 25

AMC 12

1957 AMC 12 Problem 19 • 1959 AMC 12 Problem 11 • 1962 AMC 12 Problem 36 • 1975 AMC 12 Problem 18 • 1984 AMC 12 Problem 9 • 2009 AMC 12B Problem 5 • 2011 AMC 12A Problem 19 • 2012 AMC 12A Problem 20 • 2016 AMC 12B Problem 7 • 2020 AMC 12A Problem 19

AIME

1993 AIME Problem 12 • 1994 AIME Problem 4 • 2006 AIME I Problem 13 • 2007 AIME I Problem 7 • 2009 AIME I Problem 8 • 2021 AIME I Problem 3 • 2021 AIME II Problem 9 • 2024 AIME II Problem 6

More number theory concepts

Chicken McNugget TheoremChinese Remainder Theoremcontinued fractiondigitsDiophantine EquationdivisibilityEuler’s Totient Functionfactorfactor countingFermat’s Little Theoremgreatest common divisorleast common multipleLegendre’s Formulamodular arithmeticmodular exponentiationmultiplemultiplicative orderpalindromeparityperfect powerperfect squareprimeprime factorizationquadratic residuesum of factorstrailing zerostriangular numberunits digit