AMC combinatorics problems
Counting techniques, permutations and combinations, recursion, bijections and graph theory. 340 problems across 27 concepts. 188 come from the AMC 10 and 152 from the AMC 12.
Picks a problem you have not seen, at about the difficulty you are handling.
Concepts in combinatorics
- Combinations54
- Counting integers in a range46
- Arrangements with restrictions37
- Multiplication principle37
- Complementary counting29
- Basic counting27
- Graph theory27
- Inclusion-exclusion24
- Permutations21
- Subsets17
- Counting intersections15
- Bijection14
- Double counting10
- Counting pairs9
- Burnside's Lemma8
- Circular arrangements8
- Multiset permutations8
- Stars and bars8
- Combinatorial game7
- Pigeonhole principle7
- Counting shapes in figures6
- Fencepost counting4
- Partitions and compositions4
- Recursive counting4
- Lattice paths3
- Tiling3
- Venn Diagram3
60 most recent problems
Newest contests first. Every problem opens with its answer choices, hints and a worked solution.
- 2025 AMC 10A · Problem 12
- 2025 AMC 10A · Problem 14
- 2025 AMC 10A · Problem 21
- 2025 AMC 10A · Problem 24
- 2025 AMC 10B · Problem 3
- 2025 AMC 10B · Problem 11
- 2025 AMC 10B · Problem 16
- 2025 AMC 10B · Problem 21
- 2025 AMC 10B · Problem 22
- 2025 AMC 12A · Problem 6
- 2025 AMC 12A · Problem 13
- 2025 AMC 12A · Problem 15
- 2025 AMC 12A · Problem 18
- 2025 AMC 12A · Problem 23
- 2025 AMC 12B · Problem 13
- 2025 AMC 12B · Problem 17
- 2025 AMC 12B · Problem 19
- 2025 AMC 12B · Problem 24
- 2024 AMC 10A · Problem 6
- 2024 AMC 10A · Problem 9
- 2024 AMC 10A · Problem 18
- 2024 AMC 10A · Problem 20
- 2024 AMC 10A · Problem 25
- 2024 AMC 10B · Problem 1
- 2024 AMC 10B · Problem 3
- 2024 AMC 10B · Problem 12
- 2024 AMC 10B · Problem 17
- 2024 AMC 10B · Problem 20
- 2024 AMC 10B · Problem 22
- 2024 AMC 12A · Problem 11
- 2024 AMC 12A · Problem 16
- 2024 AMC 12A · Problem 22
- 2024 AMC 12B · Problem 1
- 2024 AMC 12B · Problem 3
- 2024 AMC 12B · Problem 16
- 2023 AMC 10A · Problem 6
- 2023 AMC 10A · Problem 12
- 2023 AMC 10A · Problem 16
- 2023 AMC 10A · Problem 18
- 2023 AMC 10A · Problem 20
- 2023 AMC 10A · Problem 25
- 2023 AMC 10B · Problem 9
- 2023 AMC 10B · Problem 10
- 2023 AMC 10B · Problem 11
- 2023 AMC 10B · Problem 16
- 2023 AMC 12A · Problem 13
- 2023 AMC 12A · Problem 21
- 2023 AMC 12A · Problem 24
- 2023 AMC 12B · Problem 5
- 2023 AMC 12B · Problem 8
- 2022 AMC 10A · Problem 9
- 2022 AMC 10A · Problem 14
- 2022 AMC 10A · Problem 22
- 2022 AMC 10A · Problem 24
- 2022 AMC 10B · Problem 3
- 2022 AMC 10B · Problem 14
- 2022 AMC 10B · Problem 18
- 2022 AMC 12A · Problem 3
- 2022 AMC 12A · Problem 7
- 2022 AMC 12A · Problem 10
Use Start combinatorics practice above to work through the remaining 280.