Counting regions — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Counting regions — 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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More combinatorics concepts
arrangements with restrictionsbasic countingbijectionBurnside’s LemmaCatalan Numbercircular arrangementscombinationscombinatorial gamecomplementary countingcounting integers in a rangecounting intersectionscounting pairscounting shapes in figuresderangementsdouble countingfencepost countinggenerating functionsgraph theoryinclusion-exclusionlattice pathsmultiplication principlemultiset permutationspartitions and compositionsPascal’s Trianglepermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram