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Puzzles and Paradoxes

How To Really Eliminate The Staircase Paradox?

Published on January 26, 2022 by Hemanth

The staircase paradox: A staircase with a base of 4 centimetres (cm) and height of 4 cm. There are two stairs, each with a length of 2 cm and height of 2 cm.
After my original essay on the staircase paradox got considerable scientific cricitism, I had to write a technical essay explaining the mathematics behind it!
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How To Solve The Dartboard Paradox?

Published on January 23, 2022 by Hemanth

How to solve the dartboard paradox? - A picture of a dartboard with darts stuck on it.
The dartboard paradox is one of those pesky paradoxes that revolves around the concepts of zero and infinity. The notion of probability makes it trickier.
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How Much String Would You Need To Wrap The Earth?

Published on January 18, 2022 by Hemanth

How much string would you need to wrap the Earth? A picture of the planet earth surrounded by dotted pink cicle. A purple measuring line wraps around this circule with two question marks indicating that the circumference of the pink circle is unknown.
Let us say that you are to wrap the earth with a single piece of string around the equator. This math puzzle reveals an interesting aspect of human behaviour.
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Can You Really Solve The Staircase Paradox?

Published on January 17, 2022 by Hemanth

The staircase paradox: A staircase with a base of 4 centimetres (cm) and height of 3 cm. There are two stairs, each with a length of 2 cm and height of 1.5 cm. Is the total staircase length equal to 5 cm or 7 cm?
The staircase paradox is one of those challenges that deeply questions our fundamental logic. It is a geometrical problem that has occurred in varying forms.
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Why Earning More Leads To Lesser Satisfaction

Published on January 15, 2022 by Hemanth

Why earning more leads to lesser satisfaction: An illustration of the Weber–Fechner laws - On each side, the lower square contains 10 more dots than the upper square. Yet, the perception is different between the left and the right square sets. On the left, 10 dots are in the top square and 20 in the bottom one. The difference is clearly visible. On the right, the top square has 110 dots and the bottom one has 120 dots. The difference is not clearly visible.
Have you ever noticed how earning more leads to lesser satisfaction? And I don’t mean just money. This article goes explains this phenomenon using science.
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How To Solve The Doubling Puzzle?

Published on January 11, 2022 by Hemanth

The Doubling Puzzle: On the left two unhappy sheep stand before one patch of grass. Ten days later, the two sheep seem happy and are standing before two patches of grass.
The doubling puzzle has been popular among math enthusiasts for centuries now. In this article, I will be presenting a simplified version of this puzzle.
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What Is the Shortest Road Connecting 4 Cities?

Published on January 9, 2022 by Hemanth

Puzzle: Shortest Road Connecting 4 Cities. The image has 4 points: bottom left: A, bottom right: B, top right: C, and top left, D. The points together form a square that has a side length of 1 Km.
Say that you have been tasked with figuring out the shortest road connecting 4 cities. These four cities are located at the vertices of a square. What now?
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How To Make Working With Squares Fun in Math?

Published on January 9, 2022 by Hemanth

How to make working with squares fun in math
In mathematics, squares are typically defined as numbers multiplied by themselves. However, there is a more intuitive definition of a square in geometry.
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How To Run A Math Hotel With Infinite Rooms?

Published on December 25, 2021 by Hemanth

An image of a hotel with infinite rooms. The sign on top of the hotel says, "HOTEL FULL!". The stick figure of a person is standing outside the hotel with a question mark over the head.
What is so special about a math hotel with infinite rooms? For starters, it is a hotel that exists only in the mathematical world, where a game is to played!
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What Really Happens When You Invent Infinite Infinities?

Published on December 23, 2021 by Hemanth

An image asking if infinite infinities are possible
‘Infinite Infinities’ is a crazy-sounding concept. Most people have issues wrapping their heads around the concept of infinity. Why infinite infinities then?
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