The 3n+1 Problem

The 3n+1 Problem

This problem is known as Collatz Conjecture. Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two.If the number is odd, triple it and add one. The conjecture is that no matter what value of the starting number, the...
The Dhaba Problem

The Dhaba Problem

Suppose on a highway, there is a Dhaba. Name it by Dhaba A. You are also planning to set up a new Dhaba. Where will you set up your Dhaba? Model this as a Mathematical Problem. This is an interesting and creative part of the BusinessoMath-man in you. You have to...
The Organic Math of Origami

The Organic Math of Origami

Did you know that there exists a whole set of seven axioms of Origami Geometry just like that of the Euclidean Geometry? The Origami in building the solar panel maximizing the input of Solar Power and minimizing the Volume of the satellite Instead of being very...
Natural Geometry of Natural Numbers

Natural Geometry of Natural Numbers

How does this sound? The numbers 18 and 30 together looks like a chair.  The Natural Geometry of Natural Numbers is something that is never advertised, rarely talked about. Just feel how they feel! Let’s revise some ideas and concepts to understand the...
Sign Pyramid – AMC 8 2018 Problem 19

Sign Pyramid – AMC 8 2018 Problem 19

Big idea – stabilization In a counting problem, you may need to stabilize the number of cases. This means, by letting some of the variables change, one may fix the remaining cases. This is the central idea in the following problem from American Mathematical...
AMC 10 Paper Folding Geometry

AMC 10 Paper Folding Geometry

We fold a paper using GeoGebra and explore a problem from American Mathematical Contest (AMC 10) Problem: A rectangular piece of paper whose length is \( \sqrt 3 \) times the width has area A. The paper is divided into three equal sections along the opposite lengths,...