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Puzzles and Paradoxes

How To Really Solve The Kissing Circles Puzzle

Published on June 8, 2022 by Hemanth

How To Really Solve The Kissing Circles Puzzle - An illustration where on the left, three bigger circles (circles 1, 2, and 3) enclose a smaller circle (circle x), and on the right, one bigger circle (circle x) encloses three smaller circles (circles 1, 2, and 3).
I first came across the kissing circles puzzle when I was studying the topic of hyperspheres. The puzzle as such is quite simple, but it has profound insights!
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How To Really Solve This Tricky Algebra Problem? (IV)

Published on June 6, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (IV) - An image showing the following equations on the left: x² + y² = 7 and x³ + y³ = 10. On the right, the following equation is written: x + y = ??. Below this equation, the following information is provided in a box: x,y ∈ ℝ.
Welcome to the fourth entry in the tricky algebra problem series. In this entry, you get to solve a fun and challenging math olympiad level algebra problem!
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Big Tech Using Big Data For Perfect Prediction/Spying A Lie

Published on June 4, 2022 by Hemanth

Big Tech Using Big Data For Perfect Prediction/Spying A Lie - An illustration showing a stick figure on the left with a smartphone. The stick figure seems to be smiling as it is texting. Labelled above the stick figure is the text "You". On the right, a much bigger stick figure seems to be using a telescope to spy on what the smaller stick figure is typing. Labelled above this stick figure is the text "Big Tech".
The notion of big tech using big data to predict human behavior remains an ethical concern. This essay covers the mathematics behind such prediction technology.
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How To Really Understand Order Of Operations

Published on June 2, 2022 by Hemanth

How To Really Understand Order Of Operations - An image with the following question: 12 ÷ 4 (1 + 2) = ?? Below this equation, the following text is written: "PEMDAS/BEDMAS/BODMAS"
Order of operations is a fundamental math concept that kids learn at school as BODMAS/PEMDAS. But if you blindly follow PEMDAS/BODMAS, you are taking a risk!
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How To Really Choose Between Favourite Experiences And Trying New Ones?

Published on May 31, 2022 by Hemanth

How To Really Choose Between Favourite Experiences And Trying New Ones? - An illustrative image where on the left, a restaurant named "Favourite Restaurant" is open and on the right, a restaurant named "New & Trendy Restaurant" is open. In the middle, a stick figure is seen undecided between the two restaurants with a bubble dialogue of "?"
Every day in life, you are faced with situations where you have to choose between favourite experiences and new ones. This essay uses science to solve this!
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Why Is Negative Times Negative Really Positive?

Published on May 28, 2022 by Hemanth

Why Is Negative Times Negative Really Positive? - An image showing the following equation inside a box: (-1)*(-1) = +1. Below this box, the following text is written "BUT Why??". "BUT" is in pink whereas "WHY??" is in black.
Negative times negative is positive. Everyone learns this in school and accepts it as truth. Yet, when you ask "why", insecurity floods in. Let's change that!
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How To Really Solve This Packing Spheres Puzzle?

Published on May 22, 2022 by Hemanth

How To Really Solve This Packing Spheres Puzzle? - An illustration showing a triangular structure of circles. The base has 5 circles, the next layer up has 4 circles, the next layer - 3, the next layer - 2, and the final layer - 1. The total number of circles adds up to 15.
Packing spheres is a classic geometry problem that has practical relevance as well as mathematical significance - a combination of geometry and number theory!
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How To Actually Avoid The Transposed Conditional

Published on May 20, 2022 by Hemanth

How To Actually Avoid The Transposed Conditional? - An image showing a cute little cow with black and white spots on the left and cute little dog with black and white spots on the right. The cow is standing and the dog is jumping. The cow has a pink nose and pink inner-sides of ears. Likewise, the dog has a pink belly, pink inside of its mouth and pink inside of its ears. The cow says "I have four legs. So, I'm a cow!" The dog says "I have 4 legs. So, I'm also a cow!"
The transposed conditional is another one of those subtle but very consequential misunderstandings in the field of statistics. Read the essay to learn more!
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Why Is The Hot Hand Fallacy Really A Fallacy?

Published on May 19, 2022 by Hemanth

Why Is The Hot Hand Fallacy Really A Fallacy? - An image showing a basketball rolling on the hoop of a basket. Around this picture, the following question is written: "Do you really have a hot hand?"
The hot hand fallacy is one of those phenomena that divided and rocked the scientific world. Check out the essay to learn more about this phenomenon!
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How To Really Understand Statistical Significance?

Published on May 17, 2022 by Hemanth

How To Really Understand Statistical Significance? - An illustration of a bell curve that shows the 95% confidence interval highlighted in pink. There are 3 significant values marked on the horizontal axis: -1.96 on the left boundary of the confidence interval, 0 at its centre, and +1.96 at its right boundary.
Statistical significance is one of those “scientific” concepts/tools that has steadily been misused over the years. In this essay, we clarify the issues!
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