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Puzzles and Paradoxes

Can You Really Solve This Tricky Rep-Tile Puzzle?

Published on May 3, 2022 by Hemanth

Can You Really Solve This Tricky Rep-Tile Puzzle? - An image featuring an isosceles right triangle that is subdivided into two similar isosceles right triangles that are similar to the bigger triangle. On the right hand side of the triangle, the following text is hand-written: "Two congruent triangles tile a bigger similar triangle." Below the triangle, the following text is hand-written in bold: "WHAT NEXT?"
What is a rep-tile? This essay has the answers, and what's more, poses a challenging puzzle as well. If you are into hard geometry problems, look no further!
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How To Really Solve This Tricky Algebra Problem? (II)

Published on May 2, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (II) - (8^x - 2^x)/(6^x - 3^x) = 2; x = ??
When you take a look at this, it does not come across as a tricky algebra problem at all. But think again. This problem requires mathematical rigour.
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How To Really Benefit From Curves Of Constant Width?

Published on April 27, 2022 by Hemanth

How To Really Benefit From Curves Of Constant Width? - A wooden plank placed on top of two differently shaped objects (Image from WikiCC). One object features a circular corss-section whereas the other object features a curved triangular cross-section.
Curves of constant width represent one of the most elegant real-life applications of plane geometry. If you are into plane geometry, this is for you!
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The Additive Palindrome Conjecture Is A Risky Venture

Published on April 26, 2022 by Hemanth

The Additive Palindrome Conjecture Is A Risky Venture - An image showing the following mathematical operations: 58 + 85 = 143 (not a palindrome); 143 + 341 = 484 (a palindrome).
The additive palindrome conjecture is very welcoming and satisfying as far as the underlying concept is concerned. Yet you should probably not try to prove it!
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How To Really Solve The Straight Lines And Triangles Puzzle?

Published on April 25, 2022 by Hemanth

How To Really Solve The Straight Lines And Triangles Puzzle? - An image showing four straight lines that intersect each other at a unique point. At any point of intersection, no more than two lines are involved. On top of this illustration, the following question is posed: "HOW MANY TRIANGLES?"
Straight Lines and Triangles - A simple puzzle that goes beyond geometry! Your job is to find out how many triangles you can construct using ’n’ straight lines.
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How To Really Solve This Combinatorics Puzzle?

Published on April 23, 2022 by Hemanth

How To Really Solve This Combinatorics Puzzle? - An image showing a total of thirteen planar points. Of the thirteen, six pink points are collinear. That is, they lie along a straight line (visualized as a pink broken line). Similarly, four green points and three black points are collinear along a green broken line and a black broken line respectively.
Use this combinatorics puzzle to brush up on your logical reasoning. Given the following planar points, how many straight lines can you construct using them?
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How To Execute The Quadratic Equation Magic Trick?

Published on April 21, 2022 by Hemanth

How To Execute The Quadratic Equation Magic Trick? - An image showing the following equation: ax² + bx + c. Below the equation, the following three questions are asked one below the other: a = ??; b = ??; c = ??
The quadratic equation magic trick is not your usual run-of-the-mill math trick. It raises the bar a couple of notches. Why don't you give it a try?
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How To Really Solve The Monkey And The Coconuts Puzzle?

Published on April 17, 2022 by Hemanth

How To Really Solve The Monkey And The Coconuts Puzzle? - An illustrative sketch with a cute monkey sitting like a baby on the left, and five coconuts stacked on top of each other on the right. The coconuts also look cute with goofy looking eyes and their tongues sticking out.
The monkey and the coconuts is a historically viral math puzzle that appears to be simple on the surface but is anything but. Why don't you give it a try?
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How To Really Solve This Tricky Algebra Problem?

Published on April 13, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? - An image showing the following equation on top: 10^x + 11^x + 12 ^x = 13^x + 14^x. Below this equation, the following question is raised: "x = ??"
On the surface, this does not look like a tricky algebra problem. However, it is an elusive problem. If you can analyse functions, it makes the job much easier!
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How To Casually Guess Numbers After Dice Throws?

Published on April 10, 2022 by Hemanth

How To Casually Guess Numbers After Dice Throws? - Three dice with 1, 6, and x on top. The following equation is written on top: 1+6+x = ?? What could 'x' potentially be?
Would it not be pleasing if you could casually guess numbers after dice throws? But hang on a minute! Aren’t dice throws supposed to be random?
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