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Bijection — AMC & AIME Problems

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

2025 AMC 8 Problem 16 · 2025 AMC 8 Problem 22

AMC 10

2005 AMC 10B Problem 18 · 2010 AMC 10A Problem 22 · 2012 AMC 10A Problem 23 · 2017 AMC 10B Problem 17 · 2018 AMC 10B Problem 9 · 2019 AMC 10A Problem 17 · 2021 AMC 10A Spring Problem 20 · 2024 AMC 10A Problem 25

AMC 12

2003 AMC 12A Problem 22 · 2006 AMC 12A Problem 25 · 2009 AMC 12B Problem 25 · 2012 AMC 12B Problem 18 · 2017 AMC 12B Problem 11 · 2018 AMC 12A Problem 13

AIME

2001 AIME I Problem 6 · 2006 AIME I Problem 11 · 2009 AIME II Problem 6 · 2009 AIME II Problem 9 · 2010 AIME I Problem 10 · 2011 AIME II Problem 6 · 2015 AIME I Problem 12 · 2018 AIME I Problem 10 · 2026 AIME II Problem 13

More combinatorics concepts

arrangements with restrictionsbasic countingBurnside’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 ConvolutionVenn Diagram