Double counting — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses double 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
1985 AMC 8 Problem 23 · 1999 AMC 8 Problem 11 · 2000 AMC 8 Problem 23 · 2005 AMC 8 Problem 14 · 2009 AMC 8 Problem 21 · 2020 AMC 8 Problem 16
AMC 10
2004 AMC 10A Problem 13 · 2005 AMC 10A Problem 17 · 2007 AMC 10A Problem 11 · 2023 AMC 10A Problem 6 · 2023 AMC 10A Problem 18
More combinatorics concepts
arrangements with restrictionsbasic countingbijectionBurnside’s LemmaCatalan Numbercircular arrangementscombinationscombinatorial gamecomplementary countingcounting integers in a rangecounting intersectionscounting pairscounting regionscounting shapes in figuresderangementsfencepost countinggenerating functionsgraph theoryinclusion-exclusionlattice pathsmultiplication principlemultiset permutationspartitions and compositionsPascal’s Trianglepermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram