Recursive counting — AMC & AIME Problems

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

2010 AMC 8 Problem 25

AMC 12

2007 AMC 12A Problem 25 2015 AMC 12A Problem 22 2020 AMC 12B Problem 24

More combinatorics concepts

arrangements with restrictionsbasic countingbijectionBurnside’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 principlestars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram