Combinatorics

Combinatorics is the art of counting. It deals with selections, arrangements, and combinations of objects. Questions involve determining the number of ways to perform tasks, arrange items (permutations), or choose subsets (combinations), often using principles like the product rule and sum rule.

Pigeonhole Principle Double Counting Binomial Coefficients and Pascal's Triangle Product Rule / Rule of Product Graph Theory Matchings Induction (Mathematical Induction) Game Theory Combinatorial Geometry Invariants Case Analysis / Checking Cases Processes / Procedures Number Tables Colorings

• Question

  Cut the given shape into two congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Cut the given shape into three congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Cut the given shape into three congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Cut the given shape into three congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Divide the given shape into three congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Partition the given shape into four congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries) -> Reflection

• Question

  Divide the given shape into four congruent parts:

  ​​​​​​​

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Divide the given shape into four congruent parts:

  ​​​​​​​

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Dissect the given shape into four congruent parts:

  ​​​​​​​

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)

• Question

  Dissect the given shape into four congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)