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Multiple — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Multiple — 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

1991 AMC 8 Problem 9 • 1996 AMC 8 Problem 1 • 1997 AMC 8 Problem 5 • 2005 AMC 8 Problem 18

AMC 10

2001 AMC 10 Problem 25 • 2003 AMC 10A Problem 15 • 2005 AMC 10A Problem 22 • 2005 AMC 10B Problem 13 • 2022 AMC 10B Problem 8

AMC 12

2001 AMC 12 Problem 12 • 2002 AMC 12B Problem 21 • 2003 AMC 12A Problem 18 • 2009 AMC 12A Problem 4 • 2022 AMC 12B Problem 6

AIME

2007 AIME I Problem 1 • 2007 AIME II Problem 7

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 exponentiationmultiplicative orderpalindromeparityperfect powerperfect squarepower of 2primeprime factorizationquadratic residuesum of factorstrailing zerostriangular numberunits digit