Basic counting — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Basic counting — a combinatorics 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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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

1985 AMC 8 Problem 7 1986 AMC 8 Problem 9 1998 AMC 8 Problem 11 2004 AMC 8 Problem 5 2005 AMC 8 Problem 14 2006 AMC 8 Problem 2 2009 AMC 8 Problem 9 2010 AMC 8 Problem 1 2011 AMC 8 Problem 3 2011 AMC 8 Problem 8 2013 AMC 8 Problem 22 2014 AMC 8 Problem 16 2016 AMC 8 Problem 18 2024 AMC 8 Problem 17 2026 AMC 8 Problem 2

More combinatorics concepts

arrangements with restrictionsbijectionBurnside’s LemmaCatalan Numbercircular arrangementscombinationscombinatorial gamecomplementary countingcounting integers in a rangecounting intersectionscounting pairscounting regionscounting shapes in figuresderangementsdouble countingfencepost countinggenerating functionsgraph theoryinclusion-exclusionlattice pathsmultiplication principlemultiset permutationspartitions and compositionsPascal’s Trianglepermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram