Solving Mathematical Challenges with R

In a new series of posts, I will explore how the free statistical tool R can be used to answer mathematical challenges.

Le Monde is a French daily newspaper with one of the highest circulation numbers. There used to be a small section at the very end which varied by day of the week containing a small intellectual puzzle, either a crossword, a Sudoku, a math challenge...
I haven't lived in France for quite some time, but checking online recently it appears they have slightly changed the format, adding mathematical challenges which are presented by Cedric Villani, French Mathematician and recipient of the 2010 Fields Medal (shameless fun fact, his PhD Advisor Pierre-Louis Lions and also recipient of the Fields Medal in 1994 was my math teacher during my Master's).

While these weekly challenges are mathematical in nature and can be (should be!) resolved with pen and paper, I will take a computer-oriented approach, namely with the R programming language for statistical computing. The idea is not necessarily to fully solve the challenge (computationally or not), but indirectly use these challenges as R tutorials, dig deeper into the mathematical challenges along the way, and with a focus on visualisations. Because of the focus on R, we'll also take slight detours to look into R performance, best practices, try different packages and approaches.

Think of this as a road trip, we kind of know where we want to go, but have no idea if we'll reach our destination, and much less certain of the path we'll take, but whatever the path we'll see some really cool stuff along the way!

Challenge #1: Palindromes

Challenge #2: Slicing Cubes

Challenge #3: Sum of all grids

Challenge #4: Match-ing game (coming up soon!)

Challenge #5: Winning ropes (coming up soon!)