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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).

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