combinatorics
Subsets — AMC & AIME Problems
48 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Subsets — 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Subsets and Complements - Definition & Examples.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
AMC 12
AIME
- 1983 AIME Problem 13
- 1986 AIME Problem 12
- 1988 AIME Problem 1
- 1988 AIME Problem 15
- 1989 AIME Problem 2
- 1989 AIME Problem 13
- 1991 AIME Problem 5
- 1992 AIME Problem 2
- 1992 AIME Problem 12
- 1993 AIME Problem 8
- 2002 AIME II Problem 9
- 2006 AIME I Problem 2
- 2007 AIME II Problem 10
- 2009 AIME II Problem 6
- 2010 AIME I Problem 7
- 2010 AIME II Problem 8
- 2014 AIME I Problem 5
- 2014 AIME II Problem 9
- 2017 AIME I Problem 12
- 2017 AIME II Problem 1
- 2018 AIME I Problem 9
- 2018 AIME I Problem 12
- 2021 AIME II Problem 6
- 2022 AIME I Problem 12
- 2023 AIME I Problem 11
- 2023 AIME II Problem 11
- 2024 AIME II Problem 6
- 2025 AIME II Problem 7
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 regions
- 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
- Tiling
- Tree diagram
- Vandermonde’s Convolution
- Venn Diagram