**Continue reading the story**"Menger sponge"

## Post Archives from the ‘Interesting Articles’ Category

## Menger sponge

This is not a puzzle, rather an interesting concept.
A Menger sponge is defined as follows:
1. Take a 1x1x1 cube and divide it into 27 smaller cubes like a Rubix cubes.
2. Remove the small cubes in the middle of each face, and the small cube in the center. We are left with 20 cubes.
3. Repeat steps 1,2 for each smaller cube.
4. Keep repeating this process …

## A thought experiment

A library that has every book in the world won't be so useful. Google is probably more useful. The usefulness of a library is determined by how soon you can get information you want, not by how many books are in the library. See why for yourself via this Quora article.

## Irresistible force paradox

"What happens when an unstoppable force meets an immovable object?"
It's similar in form to the Omnipotence paradox: "Can God make a stone that he cannot lift?"
Can you resolve this paradox?
- via Wikipedia

## A smart child

A physicist asked his 6 year old son to imagine standing on top of a big ball in outer space. Then, he told his son, he looks over the edge, and there is a person on the other side of the ball, upside down, with feet on the bottom of the ball. He asked his son: will that upside-down person fall off the ball? His …

**Continue reading the story**"A smart child"## Segregation

Consider an n x n grid. 30% of the cells are colored green and another 30% are colored blue at random. The remaining cells are empty. It is preferred that each colored cell has 3 neighbors (of the 8 neighbors) of the same color. Colored cells which do not have 3 same color neighbors are called "wrong". The following process occurs: At each time step, …

**Continue reading the story**"Segregation"## Integer programming

3 objects A,B and C together cost 50 cents.
B costs more than 3 times as much as A, but no more than 4 times as much.
C costs more than 6 times as much as A, but no more than 3 times as much as B.
The costs are all integers.
What are the smallest and largest prices that B can take?
This is an example of integer …

**Continue reading the story**"Integer programming"## Twin prime conjecture.

Recently, a chinese mathematician made progress towards the twin prime conjecture. For an informal introduction, read it in the news here.
I cannot resist being formal, so let me give a puzzle and explain the conjecture as well:
Let be the sequence of prime numbers and .
Exercise: Show that .
Now the twin prime conjecture states that .
We …

**Continue reading the story**"Twin prime conjecture."## Uncountability of real numbers - a simple proof

In this article, I wish to show a simple elementary proof that there cannot exist any bijection between the set of real numbers and the set of natural numbers . This proof is popularly known as Cantor's diagonal proof.
Here's the proof. Firstly I claim that there exists a bijection from the unit interval to . Note that the unit interval is the set of …

**Continue reading the story**"Uncountability of real numbers - a simple proof"