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Puzzles and Paradoxes

How To Really Solve This Fun Geometry Puzzle?

Published on July 11, 2022 by Hemanth

How To Really Solve This Fun Geometry Puzzle? A complex geometry made of 4 squares - two identical squares stacked on top of each other on the right. There are two differently-sized squares on the left that are on top of each other and touch the two squares on the right at the same time. There is a line of length 4 units joining the right-intersection of the left-sqaures and the right squares to form a triangle. The left-squares are shaded. The following text is seen: "Shaded Area = ??".
I recently came across this fun geometry puzzle and it managed to engage me. Don't let it fool you. This puzzle is much easier than it looks!
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How To Really Understand Pascal’s Wager

Published on July 8, 2022 by Hemanth

How To Really Understand Pascal's Wager - An image showing a portrait of Blaise Pascal on the left and the second edition of Pascal's Pensées on the right. At the centre is an arrow pointing from left to right.
Pascal’s wager is a theological argument made by the iconic science figure, Blaise Pascal. The plot twist is that it involves bets and scientific thinking!
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How To Really Solve This Tricky Algebra Problem? (VI)

Published on July 6, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (VI) - x + y = 41; x*y = 16; x √(x) + y √(y) = ??
Welcome to the sixth entry in the tricky algebra problem series. In this essay, you are challenged to solve a secondary-school level math olympiad problem!
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How To Really Understand Fractals?

Published on July 5, 2022 by Hemanth

How To Really Understand Fractals? - An image showing a Romanesco Broccoli on the left, and a unique triangular pattern on the right. There is an arrow point left-to-right at the centre. The triangular pattern involves a big triangle and three differently sized smaller triangles inside. Some of these triangles are shaded pink, while others are shaded white.
Fractals are generally seen as geometric shapes that self-similarly contain themselves at arbitrary scales. Learn about fractals intuitively in this essay!
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How To Intuitively Understand Buffon’s Needle Problem

Published on July 2, 2022 by Hemanth

Buffon's Needle Problem - An illustration showing four vertical lanes (with five lane boundaries) that are parallel to each other and equidistant from one another. They are spaced at a width of 'L' units. Buffon's needle appears to be at an angle in the first lane without crossing any lane boundary. The length of Buffon's needle is also 'L' units.
Buffon’s needle problem is a game that juxtaposes geometry and probability. It is a profound concept that laid the foundations of geometric probability.
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Can You Actually Solve This Viral Geometry Puzzle? (II)

Published on June 28, 2022 by Hemanth

Can You Actually Solve This Viral Geometry Puzzle? (II) - An illustration featuring a right-angled isosceles triangle with two equal sides of length 4 units each. Inside the triangle is an inscribed circle touching all three sides of the triangle. Inside the circle is also the following text: "Area of Circle = ??" The two equal sides are at right-angles to each other on second vertex from the left.
In this essay, I have yet another viral geometry puzzle for you. You need to work out the area of the inscribed circle. Here's a hint to solve it: use tangents!
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How To Design A Franc-carreau or Fair-square Game

Published on June 20, 2022 by Hemanth

How To Design A Franc-carreau or Fair-square Game - An illustration showing a 6x6 square grid with a circular pink coin inside one of the grids without touching any grid lines, and a circular green coin that touches four grid lines. Pink coin → Win; Green coin → Loss
The Franc-Carreau or fair-square is a game of chance that juxtaposes geometry and probability. It is considered to be the origin of geometric probability!
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Can You Actually Solve This Viral Geometry Puzzle?

Published on June 19, 2022 by Hemanth

Can You Actually Solve This Viral Geometry Puzzle? - A square with a point inside that connects to the mid-point of each side such that the square splits into four uneven areas. Top-left area = 10 cm²; top-right area = 16 cm²; bottom-left area = 8 cm²; bottom-right area = ??
I recently came across this viral geometry puzzle on the web, and found it interesting. All you need is the following hint to solve this puzzle: triangles!
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How To Really Solve This Tricky Algebra Problem? (V)

Published on June 16, 2022 by Hemanth

How To Really Solve This Tricky Algebra Problem? (V) - (x²/y²) + (y²/x²) = 287; [(x/y) + (y/x)]³ = ??; x not equal to zero; y not equal to zero
Welcome to the fifth entry in the tricky algebra problem series. This one is aimed at beginners. Can you solve this challenge in under one minute?
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How To Actually Solve The Königsberg Bridge Problem?

Published on June 9, 2022 by Hemanth

The Königsberg Bridge Problem - An illustration showing seven brdiges connecting four landmasses. Island 1 (centre) is connected to the upper bank (north) and the lower bank (south) via two bridges each. Island 1 and Island 2 (east) are connected by a bridge. Island 2 is connected to the upper bank and the lower bank via one bridge each.
The Königsberg bridge problem started as a logic puzzle to the city's residents. It laid the foundations for new math fields such as graph theory and topology!
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