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# Problem Garden

Mathematics is not a spectator sport. In this portal, we have gathered (and are adding) problems, discussions and challenges that you may try your hands on.

## ISI BStat 2018 Subjective Problem 2

Sequential Hints: Step 1: Draw the DIAGRAM with necessary Information, please! This will convert the whole problem into a picture form which is much easier to deal with. Step 2: Power of a Point - Just the similarity of $$\triangle QOS$$ and $$\triangle POR$$ By the...

## ISI BStat 2018 Subjective Problem 1

The solution will be posted in a sequential hint based format. You have to verify the steps of hints. Sequential Hints: Step 1: Solution set of sin($$\frac{x+y}{2}$$) = 0 is {$${x + y = 2n\pi : n \in \mathbb{N}}$$}- A set of parallel straight lines. The picture looks...

## A Math Conversation – I

Inspired by the book of Precalculus written in a dialogue format by L.V.Tarasov, I also wanted to express myself in a similar fashion when I found that the process of teaching and sharing knowledge in an easy way is nothing but the output of a lucid discussion between...

## 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

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

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 numbers also have a natural geometry of their. This post is about how they look in practice.

## Really understanding Barycentric coordinates

Sometimes we are interested in the relative position of a point with respect to a triangle. Is it close to the vertices? Is it closer to one of the sides compared to the other sides? This brings home the notion of mass point coordinates or barycentric coordinates.

## Problem Solving Marathon Week 2

We are having a full fledged Problem Solving Marathon. We are receiving wonderful responses from the end of our students which is making the session more and more alluring day by day. Here we are providing the problems and hints of "Problem Solving Marathon...

Problems and discussions from various math olympiads including RMO, INMO (India), USAMO, AMC (United States), BMC and more.

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#### Informative Articles

Selected articles on books, learning methods, and scholarship opportunities.

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#### ISI and CMI Entrance Solutions and Problems

Problems and Solutions from Test of Mathematics at 10+2 Level, previous year ISI and CMI Entrances.

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#### College Mathematics

Problems and discussions from TIFR, M.Math, Subject GRE, IIT JAM and more.

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