Combinatorics Cave

Levels 47–99 · combinatorics

A deep cave of infinite arrangements. Count permutations and combinations to find the way out.

Study Before You Play

Brush up on these topics to sharpen your skills for this zone.

The Counting Principle

Learn the Fundamental Counting Principle to count outcomes of multi-step events using multiplication.

Combinations & Permutations

Master counting principles, permutations, combinations, and advanced counting techniques.

Pascal's Triangle

Explore Pascal's Triangle — its construction, patterns, and connection to combinations and the binomial theorem.

Permutations & Combinations

Learn to count ordered and unordered arrangements and apply them to probability.