Pascal’s Triangle — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Pascal’s Triangle — 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

2020 AMC 8 Problem 21

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 compositionspermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram