The Chinese IMO team eat sequences like this for breakfast!* — When it comes to Olympiad Mathematics, China rules. The Chinese team has won the IMO (International Mathematical Olympiad) for the last 4 years, and has not finished outside the top 3 in the last 25 years. China runs its National Olympiad earlier than most countries. All countries run it early…

From Gauss and the birth of statistics to modern data science and machine learning — Ordinary least squares (OLS) regression is one of the first items on the menu in an introductory Statistics or Data Science course. But why do we need to square the errors? It’s a common question even high school students ask. …

Finding the Packing Chromatic Number of an Infinite Square Grid — Introducing the Packing Coloring Problem Can you fill in a 6 by 6 square grid with integers 1 to 9, such that the taxicab distance between each value of k is greater than k? Taxicab distance allows vertical or horizontal moves only. …

2022 Putnam Exam — Session A Problem 1 — As a teacher of high school mathematics, I enjoy challenging myself with High School Math Olympiad questions. But, given that memories from my undergraduate math degree are hazy at best, I’ve never been brave enough to attempt questions from the Putnam. The William Lowell Putnam Mathematical Competition… is widely considered…

Searching for philosophical truth, Frank Ramsey just happened to launch a new branch of discrete mathematics — Ramsey’s Theorem Ramsey’s Theorem is usually presented today as a statement about graphs. If you have a large enough complete graph and you color all the edges either red or blue, you will always end up with a group of vertices whose connecting edges are all the same color (a clique). There…

A nice number theory problem wrapped in a shiny wrapper. — So I’m sitting in a circle with my classmates. There are 10 of us in the circle and I’m in 2nd place. The teacher starts walking around the circle… she gives a candy to student 1 then she skips me and gives a candy to student 3. then she skips…

The battle for AI supremacy: can Google reclaim the top spot? — Ever since November 2022 when OpenAI took the tech world by storm with the launch of ChatGPT, Google has appeared to be playing catch-up. Google released its competitor Bard in March 2023, around the same time that OpenAI upgraded ChatGPT from GPT-3.5 …

Assessing the intelligence of the world’s most powerful AI system — Can you believe that GPT-4 has been out in the world for just over one month!? 😲😵🤯 It has already made such monumental waves that the “Pause Giant AI Experiments” petition now has been signed by almost 30,000 people, fearing the dangers of a rapidly evolving super-human intelligence. How intelligent is GPT-4? The “Sparks…

Find the area of the triangle. — You have 3 square Lego pieces: one square with 1 stud, one square with 4 studs, and one square with 9 studs. If you were to line up the bases of the 3 squares and inscribe them in a triangle as shown above, what would be the area of the…