Logo for LIVE by Po-Shen Loh

LIVE

English

Pigeonhole principle — AMC & AIME Problems

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

1988 AMC 8 Problem 16 · 1990 AMC 8 Problem 19 · 1994 AMC 8 Problem 21 · 2005 AMC 8 Problem 16 · 2026 AMC 8 Problem 22

AMC 10

2006 AMC 10A Problem 20 · 2010 AMC 10B Problem 3 · 2011 AMC 10B Problem 11 · 2019 AMC 10A Problem 4

AMC 12

2018 AMC 12A Problem 12 · 2018 AMC 12B Problem 10 · 2019 AMC 12A Problem 3

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 compositionsPascal’s Trianglepermutationsrecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram