Tag: puzzles


4x4 Rubik's Cube: Part 4: Sequence Order

Posted in Rubiks Cube

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This is Part 4 of a 4-part blog post on the mathematics of the 4x4 Rubik's Cube, its relation to algorithms, and some curious properties of Rubik's Cubes.

See Part 1 of this blog post here: Part 1: Representations

See Part 2 of this blog post here: Part 2: Permutations

See Part 3 of this blog post here: Part 3: Factoring Permutations

You are currently reading Part 4 of this blog post: Part 4: Sequence Order

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Tags:    rubiks cube    combinatorics    permutations    python    puzzles    art of computer programming    knuth   


4x4 Rubik's Cube: Part 3: Factoring Permutations

Posted in Rubiks Cube

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This is Part 3 of a 4-part blog post on the mathematics of the 4x4 Rubik's Cube, its relation to algorithms, and some curious properties of Rubik's Cubes.

See Part 1 of this blog post here: Part 1: Representations

See Part 2 of this blog post here: Part 2: Permutations

You are currently reading Part 3 of this blog post: Part 3: Factoring Permutations

See Part 4 of this blog post here: Part 4: Sequence Order

Table of Contents



Tags:    rubiks cube    combinatorics    permutations    python    puzzles    art of computer programming    knuth   


4x4 Rubik's Cube: Part 2: Permutations

Posted in Rubiks Cube

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This is Part 2 of a 4-part blog post on the mathematics of the 4x4 Rubik's Cube, its relation to algorithms, and some curious properties of Rubik's Cubes.

See Part 1 of this blog post here: Part 1: Representations

You are currently reading Part 2 of this blog post: Part 2: Permutations

See Part 3 of this blog post here: Part 3: Factoring Permutations

See Part 4 of this blog post here: Part 4: Sequence Order

Table of Contents



Tags:    rubiks cube    combinatorics    permutations    python    puzzles    art of computer programming    knuth   


4x4 Rubik's Cube: Part 1: Representations

Posted in Rubiks Cube

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This is Part 1 of a 4-part blog post on the mathematics of the 4x4 Rubik's Cube, its relation to algorithms, and some curious properties of Rubik's Cubes.

You are currently reading Part 1 of this blog post: Part 1: Representations

See Part 2 of this blog post here: Part 2: Permutations

See Part 3 of this blog post here: Part 3: Factoring Permutations

See Part 4 of this blog post here: Part 4: Sequence Order

Table of Contents



Tags:    rubiks cube    mathematics    combinatorics    permutations    python    puzzles   


Shortest Lattice Paths and Multiset Permutations

Posted in Mathematics

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The Lattice Paths Problem

I first came across the lattice paths problem in Project Euler problem 15. The question described a 2x2 square lattice, and illustrated the 6 ways of navigating from the top left corner to the bottom right corner by taking the minimum number of steps - 2 right …