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

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

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