Combinatorial game — AMC & AIME Problems

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

2020 AMC 10B Problem 16 · 2021 AMC 10B Spring Problem 24 · 2023 AMC 10B Problem 10

More combinatorics concepts

arrangements with restrictionsbasic countingbijectionBurnside’s LemmaCatalan Numbercircular arrangementscombinationscomplementary 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