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Palindrome — AMC & AIME Problems

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

1988 AMC 8 Problem 25 • 2002 AMC 8 Problem 4 • 2019 AMC 8 Problem 13

AMC 10

2009 AMC 10A Problem 5 • 2009 AMC 10B Problem 11 • 2010 AMC 10A Problem 9 • 2010 AMC 10B Problem 21 • 2020 AMC 10B Problem 6

AMC 12

1991 AMC 12 Problem 17 • 1999 AMC 12 Problem 9 • 2007 AMC 12B Problem 21 • 2010 AMC 12A Problem 6 • 2010 AMC 12B Problem 11 • 2013 AMC 12A Problem 22 • 2014 AMC 12A Problem 15

AIME

2002 AIME I Problem 1 • 2021 AIME II Problem 1 • 2023 AIME II Problem 2 • 2026 AIME I Problem 2

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 orderparityperfect powerperfect squarepower of 2primeprime factorizationquadratic residuesum of factorstrailing zerostriangular numberunits digit