combinatorics
Counting intersections — AMC & AIME Problems
33 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Counting intersections — 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.
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AMC 8
AMC 10
AMC 12
- 1963 AMC 12 Problem 27
- 1965 AMC 12 Problem 4
- 1968 AMC 12 Problem 30
- 1969 AMC 12 Problem 18
- 1970 AMC 12 Problem 26
- 1971 AMC 12 Problem 17
- 1973 AMC 12 Problem 29
- 1976 AMC 12 Problem 28
- 1981 AMC 12 Problem 18
- 1983 AMC 12 Problem 2
- 1985 AMC 12 Problem 10
- 1985 AMC 12 Problem 19
- 1999 AMC 12 Problem 12
- 2002 AMC 12B Problem 14
- 2007 AMC 12A Problem 24
- 2012 AMC 12A Problem 25
- 2014 AMC 12A Problem 24
- 2018 AMC 12B Problem 24
- 2019 AMC 12A Problem 8
- 2021 AMC 12B Fall Problem 19
- 2025 AMC 12B Problem 24
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 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
- Subsets
- Tiling
- Tree diagram
- Vandermonde’s Convolution
- Venn Diagram