Counting regions — AMC & AIME Practice Problems

Counting regions — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses counting regions — 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).

AIME

2022 AIME II Problem 9 · 2025 AIME I Problem 13

More combinatorics concepts

arrangements with restrictions basic counting bijection Burnside’s Lemma Catalan Number circular arrangements combinations combinatorial game complementary counting counting integers in a range counting intersections counting pairs counting shapes in figures derangements double counting fencepost counting generating functions graph theory inclusion-exclusion lattice paths multiplication principle multiset permutations partitions and compositions Pascal’s Triangle permutations pigeonhole principle recursive counting stars and bars subsets tiling tree diagram Vandermonde’s Convolution Venn Diagram