# The Josephus Problem: Part 3: Solving the Double Step Case

Posted in Computer Science

This is Part 3 of an N-part series.

## Solving the Double Step Case

The Josephus Problem for a …

# The Josephus Problem: Part 2: Two Examples

Posted in Computer Science

This is Part 2 of an N-part series.

## Two Examples

In this blog post we'll walk through two examples of …

# The Josephus Problem: Part 1: The Problem

Posted in Computer Science

This is Part 1 of an N-part series.

## The Josephus Problem and Variations

The following problem, Cat and Mice, is Puzzle 88 in Boris Kordemsky's The Moscow Puzzles.

Purrer has decided to take a nap. He dreams …

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

Posted in Rubiks Cube

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

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

Posted in Rubiks Cube

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

# 4x4 Rubik's Cube: Part 2: Permutations

Posted in Rubiks Cube

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

# 4x4 Rubik's Cube: Part 1: Representations

Posted in Rubiks Cube

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

# Shortest Lattice Paths and Multiset Permutations

Posted in Mathematics

## 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 …