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Lattice paths — AMC & AIME Problems

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

2013 AMC 8 Problem 21 · 2014 AMC 8 Problem 11 · 2020 AMC 8 Problem 21 · 2025 AMC 8 Problem 25

AMC 10

2012 AMC 10B Problem 25

AMC 12

2003 AMC 12A Problem 22 · 2010 AMC 12A Problem 18

AIME

2002 AIME II Problem 12 · 2005 AIME I Problem 13 · 2019 AIME I Problem 5 · 2024 AIME I Problem 6 · 2026 AIME II Problem 2

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-exclusionmultiplication principlemultiset permutationspartitions and compositionsPascal’s Trianglepermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram