What an analysis of 7 million Wordle games tells us about word difficulty in light of recent adjustments by the New York Times — There have been quite a few stories about whether Wordle has changed since its recent acquisition by the New York Times. Some people have claimed that it has become more difficult and speculation has been growing about whether the NYT have modified the gameplay to make it more challenging. …

A visual data-driven exploration of the decimal expansions of fractions of the form 1/n — The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful … G. H. Hardy I watched another great Numberphile video last week. In it Brady spoke with Matt Henderson about more of his fascinating visualisations of numbers. …

Caution! This post contains some Wordle spoilers — Ok, full disclosure: I didn’t actually play a million games of Wordle, but I wrote a Wordle simulator that did. Why? Because I wanted to learn more about the dynamics of the game and evaluate some of the strategies that people have been discussing online, especially those that discuss the…

What an analysis of tweets reveals about Wordle, its words and its players. — In this post I analyse >3M Wordle tweets posted between December 23, 2021 and January 27, 2022 to show the following Wordle continues to be popular on Twitter, but much of the daily growth is due to returning players posting their latest efforts; the number of new daily players posting…

A Large-Scale Data Analysis of the Performance Costs of Training Disruptions when Preparing for the Marathon — TLDR; More than 50% of runners experience at least a 7-day break from running when training for a marathon. Longer training disruptions (≥7 days) also occur frequently. But there is hope because even a long disruption does not have to ruin your marathon. However, disruptions do come with a cost, and…

A Large-Scale Data Analysis of ~70 Million Games of Wordle — Recently I have been exploring various aspects of the popular word-game Wordle [62–67], which took the Internet by storm in January and February 2022 [12]. As I came to appreciate some of the many data science questions being asked about it, I decided to use Wordle as a case-study project…

A Visual Exploration of the Data of the Collatz Conjecture — There is a maths problem that is so simple even a first-grader can understand it, but so complicated that the world’s greatest mathematicians have warned others away from it. It starts like this. Pick a number. If it’s even, divide it by 2. If it’s odd, multiply it by 3…

Using the Online Encyclopedia of Integer Sequences (OEIS) as a Data Science Oracle in the Domain of Number Theory — As previously discussed here (and here and here) I have recently being enjoying myself using the tools of data science to explore the field of number theory. Since I am no number theory expert, this has forced me to confront an interesting, challenging, and familiar question, namely:

Explorations in number theory using the tools and techniques of data science — “”Mathematics is the queen of the sciences and number theory is the queen of mathematics.” – Carl Friedrich Gauss Number theory is a fascinating branch of pure mathematics. It is concerned with the properties of, and the relationships between, the integers. The history of number theory is populated by some…