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# Cheenta. Passion for Mathematics.

Pause for a moment! Think…

Suppose ABC be a triangle with side lengths 3, 4, 5.

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We are building a beautiful seesaw. It has three seats at A, B and C respectively. The fulcrum of the seesaw is at incenter of the triangle.

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What masses should we put at A, B and C to balance the seesaw?

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#### What is Cheenta?

Cheenta delivers outstanding programs in Mathematics for Olympiads, I.S.I. & C.M.I. Entrance and College.

Since 2010, we have worked with hundreds of students from India, United States, UK, Australia, Singapore and Middle East

All of our classes are delivered exclusively live and online. Our main center in Calcutta (India) office hosts a reading facility for advanced learners.

#### Who are Teaching?

We have ex-Olympians and outstanding researchers who teach out of love for the subject.

In India: Indian Statistical Institute, Chennai Mathematical Institute, IISER, TIFR, Calcutta University, IIT KGP

Outside India: the University of Wisconsin Milwaukee (USA), University of North Carolina (USA), St. Louis University (USA), IMPA (Brazil), E’Cole (France)

#### Admission and eligibility

Admission to a Cheenta program is highly selective. The prospective student must first go through a trial class.

Our courses are significantly more intense than regular school or college programs. Apply only if you are thrilled by the beauty of mathematics.

Math Olympiad, I.S.I. Entrance and College Mathematics candidates form the core student body of Cheenta.

## The Product of Digits, ISI Entrance 2017, Subjective Solution to problem – 5.

Understand the problem Let $$g : \mathbb{N} \to \mathbb{N}$$ with $$g(n)$$ being the product of digits of $$n$$. (a) Prove that $$g(n)\le n$$ for all $$n \in \mathbb{N}$$ . (b) Find all $$n \in \mathbb{N}$$ , for which $$n^2-12n+36=g(n)$$....

## Three Primes, ISI Entrance 2017, Subjective solution to Problem 6.

Understand the problemLet $$p_1,p_2,p_3$$ be primes with $$p_2\neq p_3$$, such that $$4+p_1p_2$$ and $$4+p_1p_3$$ are perfect squares. Find all possible values of $$p_1,p_2,p_3$$.  Start with hintsDo you really need a hint? Try it first!Let $$4+p_1p_2=m^2$$ and...

## System of n equations, ISI Entrance 2008, Solution to Subjective Problem No. 9.

Understand the problem For $$n\ge3$$, determine all real solutions of the system of $$n$$ equations : $$x_1+x_2+\cdots+x_{n-1}=\frac{1}{x_n}$$ ...

## C.M.I. 2019 Entrance – Answer Key, Sequential Hints

CMI (Chennai Mathematical Institute) Entrance 2019, Sequential hints, answer key, solutions.

## A Trigonometric Substitution, ISI Entrance 2019, Subjective Solution to Problem – 6 .

Understand the problem For all natural numbers$$n$$, let $$A_n=\sqrt{2-\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}$$ ($$n$$ many radicals) (a) Show that for $$n\ge 2, A_n=2\sin \frac{π}{2^{n+1}}$$. (b) Hence, or otherwise, evaluate the limit ...

## Two Similar Triangles, ISI B.Math/B.Stat Entrance 2018, Subjective Solution of Problem No. 2

Understand the problemSuppose that $$PQ$$ and $$RS$$ are two chords of a circle intersecting at a point $$O$$ , It is given that $$PO=3$$ cm and $$SO=4$$ cm . Moreover, the area of the triangle $$POR$$ is $$7 cm^2$$ . Find the are of the triangle $$QOS$$ . I.S.I....

## Pythagorean Triple, ISI B.Math/B.Stat Entrance 2018, Subjective Solution of Problem No. 7

Understand the problem Let $$a,b,c \in \mathbb{N}$$ be such that $$a^2+b^2=c^2$$ and $$c-b=1$$.Prove that (i) $$a$$ is odd,(ii) $$b$$ is divisible by 4,(iii) $$a^b+b^a$$ is divisible by $$c$$.   I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance...

## Investigating local connectedness of boundary of relatively hyperbolic groups – 1

This is an update from Cheenta Research Track (Geometric Group Theory group). The group is comprised of Ashani Dasgupta, Sambuddha Majumdar. Learn more about Research Track here. Reference Texts: Metric Spaces of Non-Positive Curvature by HaefligerAlgebraic Topology...

## Powers of 2 – I.S.I. B.Math/B.Stat Entrance 2019 Subjective Solution Problem 1

Understand the problem Prove that the positive integers $$n$$ that cannot be written as a sum of $$r$$ consecutive positive integers, with $$r>1$$ ,are of the form $$n=2^l$$ for some $$l\ge 0$$.   I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance...

## I.S.I. M.Math Entrance 2019 (PG) Solutions, Hints, and Answer Key

This is a work in progress. Please suggest improvements in the comment section.Problems Objective I.S.I. M.Math Subjective 2019 Objective Section (Answer Key)  1. C 2. D 3. B 4. C 5. A 6. D 7. B 8. D 9. D 10. D 11. A 12. B 13. B 14. A 15. C 16. A 17. C 18. A 19....

An advanced program in Mathematics for brilliant school students. Taught by ex-Olympians and active researchers in Mathematics.

By the way, are you interested in the fourth dimension? Here is a beauty to behold! Tetracube created the beautiful image of the Omnitruncated tesseract.

# Training brilliant minds.

Since 2010.

Cheenta has worked with brilliant maths and science olympiad students from over 6 countries. Our courses are specifically geared toward students with an exceptional interest in Mathematical Sciences.

Outstanding mathematics program for deserving school students.

#### Pre-Olympiad Thousand Flowers

For children who are starting out in Mathematics and Science.

#### I.S.I. & C.M.I. Entrance

For B.Stat and B.Math entrance at Indian Statistical Institute, B.Sc. Math at C.M.I. & KVPY.

#### College Mathematics

For I.S.I. M.Math, Mathematics Subject GRE, TIFR; Groups Analysis, Topology and more

# I.S.I. & C.M.I. Entrance

B.Stat, B.Math Entrance at I.S.I. and B.Sc. Math Entrance at C.M.I. require special training in Number Theory, Geometry, Combinatorics and Algebra (apart from regular High School topics).

Problems from standard topics such as Calculus, Trigonometry or Coordinate geometry can significantly tricky.

Number Theory, Combinatorics, Algebra, and Geometry at Olympiad standard are both necessary and useful components of this course.

#### Regular High School Topics

Advance problems from Calculus, Trigonometry, Coordinate Geometry and Algebra are bread and butter for handling more complicated ones.

# Not a spectator sport.

Think about the interesting problem!

# College Mathematics

An advanced program for College Students as well as adults interested in modern mathematics. This program is useful for I.S.I. M.Math Entrance, Subject GRE, IIT JAM and similar entrances.

We work on Groups, Rings, Fields, Linear Algebra, Analysis, Topology and other advanced topics. As usual problem solving remains the driving force of the program.

The hyperbolic 3 space may come up in this course. Behold this beautiful Hyperideal Honeycomb created by Royce3 (under creative commons).

#### Continuing Education

Many adults, who are pursuing jobs or industry, have taken this program. A curious mind, coupled with a determination to take up challenges is sufficient.

#### Advanced GRE, TIFR, M.Math

This program is for the true math fanatic, who yearn to understand the anatomy of ‘reason’ a little better. Advanced problem-solving session every week!

# What is Torsion?

Geometry is everywhere. Enjoy this bit.

# Testimonials…

“a wide range of mathematical topics, and every lesson is packed with insights and methods. We are extremely pleased with the difference he has been making. Under his tutelage Sam has secured several gold awards from the UK Mathematics Trust (UKMT)and Scottish Mathematical Council (SMC).”

Jayanta Majumdar

Glasgow, UK

“Shuborno has been studying under Ashani from last one year. During this period, we have seen our son grow both intellectually and emotionally. His concepts and approach towards solving a problem has become more mature now. Not that he can solve each and every problem but he loves to think on the tough concepts. For this, all credit goes to Ashani, who is never in a hurry to solve a problem quickly. Rather he tries to slowly build the foundation..”

Shubrangshu Das

Bangalore, India

“Our experience with Cheenta has been excellent. Even though my son started in Middle School, they understood his Math level and took personal interest in developing a long-term plan considering his strengths and weakness areas. Through out the semester courses they have nourished him with challenging problems and necessary homework. His guidance has helped my son to perform well at competitions including USAJMO and others. He has grown more confident in his math abilities over the past year and half and is hoping to do well in the future.

I am impressed with their quality and professionalism. We are very thankful to Cheenta and hope to benefit from them in the coming years. I would strongly recommend them to any student who wants to learn Math by doing challenging problems, specially if they are looking for Math than what their school can offer.”