Category: Math Puzzles
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What Is The Area Of The Square?
The circle has a radius 1. The diagonal of the square extends to be a tangent of the circle. The circle touches the black lines at three points as shown. Find the area of the square. Once again, this is a good moment to pause the article and give the problem a go yourself. When…
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A Critique of The Dark Night of Mathematics by Kirwin Hampshire
The following is a Substack essay on the existential implications of AI for mathematics by Kirwin Hampshire. In this post I am going to offer my critique of the arguments presented. The Dark Night of Mathematics What are we really doing? I am going insane. During the last week or so LLMs have produced a…
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How Would You Tether Your Goat?
A goat is tethered to the edge of a circular paddock, with a lead adjusted so that the goat can eat just half of the field. So can you tell us how long the tether must be? Here’s a smoother paraphrased version that preserves the meaning while reading more naturally: At first glance, it seems…
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A Maths Puzzle About Pirates Shooting In A Circle🏴☠️
Here’s a classic maths retold: 1,024 pirates stand shoulder to shoulder in a circle, numbered 1 through 1,024. On the captain’s whistle, the 1st pirate shoots the 2nd, the 3rd shoots the 4th, and so on around the ring — every shooter spares the one beside them and fells the one just past. The fallen…
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Let’s Look At This 2026 Maths Exam For Gifted Students In Iraq
I was scrolling on Reddit today and came across this difficult maths exam from Iraqi High School for gifted students. As someone who has completed a 3-year undergraduate degree in mathematics, I’d say similar problems also appeared on my first year exams in multivariable calculus and differential equations. Somehow it’s more ‘satisfying’ to do calculus-based…
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Can You Solve This Classic Geometry Puzzle?
I was browsing through Twitter and came across this very interesting problem by @Pratik Matematik. There are two ways to solve it, one using geometry, the other relying on trigonometric formulas! Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the…
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Twin Stars: Deng Yu, Hong Wang, and the Proofs That Moved a Century-Old Mountain
On July 23, 2026, at the International Congress of Mathematicians in Philadelphia, the Fields Medal went to four mathematicians. Two of them, Deng Yu and Hong Wang, share more than a stage. They share a classroom. Both entered Peking University’s School of Mathematical Sciences in 2007, and nearly two decades later they became the first…
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How To Find The Arc Length And Its Surface Area?
In this article, we will take a deep dive into the derivations of the arc length of a curve and the surface area of the revolution of a curve. Without further ado, let’s dive in! If you have been enjoying the content on our blog, consider checking out our website here. I have made some…
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Do You Think You Can Study Maths At Oxford University?
The function f, defined for whole positive numbers, satisfies f(1) = 1 and also the following rules f(2n) = 2f(n) and f(2n + 1) = 4f(n) The question is, how many numbers n satisfy f(n) = 16? Once again, this is a good moment to pause the article and give the problem a go yourself.…