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Venn Diagram — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Venn Diagram — 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

1991 AMC 8 Problem 23 · 1999 AMC 8 Problem 9 · 2007 AMC 8 Problem 13 · 2019 AMC 8 Problem 11

AMC 10

2000 AMC 10 Problem 21 · 2009 AMC 10A Problem 18 · 2011 AMC 10A Problem 6

AIME

2010 AIME I Problem 7 · 2014 AIME II Problem 2 · 2024 AIME II Problem 1

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 principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s Convolution