Category: Math Puzzles
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Can you find the 3 Areas? 🟦🟧🟥
The figure above shows a unit square target for shooting on the rectangular coordinate plane. The target is divided into three regions 1, 2 and 3 by two curves as shown. Find the area of the three regions. Once again, this is a good moment to pause the article and give the problem a go…
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Actually You Will Never Be Correct: A Tricky Question From MIT Puzzle Club
I have seen this maths puzzle circulating on the internet for the umpteenth time. It gets a little boring at this point. But perhaps this is the first time you’ve come across it through our blog. At first glance, it looks almost insultingly simple. There are four multiple-choice answers, so your brain immediately starts reaching…
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You Roll These Dice. Which Outcome Is More Likely?
Either you roll a 12-sided fair die once. Either you roll a 6-sided fair die twice. So in which game are you more likely to get a total of 12? Or are they both equally likely? Once again, this is a good moment to pause the article and give the problem a go yourself. When…
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So Which Outcome Is More Likely? A or B? Or Both?
Here’s a fun teaser for you. Consider the following scenarios: So can you tell me which outcome is more likely? Or are they of equal odds? 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 solution. And if you…
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An American President’s Proof of The Pythagorean Theorem
US President: James A Garfield As the 20th President of the United States in 1881, James Garfield came up with an elegant proof of the Pythagorean Theorem in 1876 while being a Congressman. His proof of this well-known theorem was later published in the New England Journal of Education Without further ado, let’s dive in! a²…
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How Would YOU Find The Total Shaded Area?
This is another geometry puzzle by Catriona Agg on X. Both the regular hexagons have area 6. What’s the total shaded area? 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 solution. And if you come up with your…
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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…