combinatorics
Lattice paths — AMC & AIME Problems
15 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Lattice paths — 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: Combinatorics with Pascal's Triangle.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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AMC 10
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
- 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