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Circular arrangements — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Circular arrangements — 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).

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

2011 AMC 8 Problem 12

AMC 10

2008 AMC 10B Problem 21 • 2014 AMC 10B Problem 24 • 2025 AMC 10A Problem 14

AMC 12

1989 AMC 12 Problem 24 • 2014 AMC 12B Problem 18 • 2015 AMC 12A Problem 17 • 2015 AMC 12B Problem 22 • 2025 AMC 12A Problem 6

AIME

2011 AIME I Problem 5 • 2011 AIME II Problem 12 • 2012 AIME II Problem 14 • 2014 AIME II Problem 9 • 2019 AIME II Problem 5

More combinatorics concepts

arrangements with restrictionsbasic countingbijectionBurnside’s LemmaCatalan Numbercombinationscombinatorial 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