combinatorics
Recursive counting — AMC & AIME Problems
21 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Recursive counting — 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 problems are used with official legal permission of the Mathematical Association of America (MAA).
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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.
1600
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2400
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3200
3600
AMC 10
AIME
- 1990 AIME Problem 9
- 2001 AIME I Problem 14
- 2002 AIME II Problem 12
- 2004 AIME I Problem 15
- 2005 AIME I Problem 13
- 2006 AIME I Problem 11
- 2008 AIME I Problem 11
- 2015 AIME II Problem 10
- 2015 AIME II Problem 12
- 2016 AIME II Problem 12
- 2018 AIME I Problem 14
- 2018 AIME II Problem 11
- 2019 AIME II Problem 12
- 2021 AIME II Problem 8
- 2025 AIME I Problem 15
- 2026 AIME I Problem 15
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
- Stars and bars
- Subsets
- Tiling
- Tree diagram
- Vandermonde’s Convolution
- Venn Diagram