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# OUTSTANDING MATHEMATICS FOR BRILLIANT STUDENTS

#### Pause.... think.

Suppose ABC is any triangle. D be any point on AB. Can you find a point X on BC such that area of triangle XAD is equal to the area of triangle ACX? Hint: Area and midpoint are intimately related.

# Three Outstanding Programs

for brilliant students

Advanced number theory, geometry, combinatorics, and algebra. This problem driven, rigorous program is taught by olympians, researchers who are active mathematicians at leading universities around the world.

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

B.Stat and B.Math Entrance Program at Indian Statistical Institute and B.Sc. Math Entrance at Chennai Mathematical Institute require special training in topics like number theory, geometry and combinatorics This rigorous program for high school students is taught by students and alumni of I.S.I. & C.M.I.

### College Mathematics Program

Entrances of TIFR, I.S.I. M.Math and Subject GRE require advanced training in topology, analysis, abstract and linear algebra. This advanced program is designed to take you ‘inside’ the beauty of mathematics.

## Group class + One-on-One

Brilliant mathematics … personalized

Step 1

#### Group Lectures

Brilliant Faculty members. Problem driven sessions.

Step 2

#### One-on-One

One mentor – one student.

Step 3

#### Problem Lists

Inspiring problems every week. Mentors help students to solve.

We contacted Cheenta because our son, Sambuddha (a.k.a. Sam), seemed to have something of a gift in mathematical/logical thinking, and his school curriculum math was way too easy and boring for him. We were overjoyed when Mr Ashani Dasgupta administered an admission test and accepted Sam as a one-to-one student at Cheenta. Ever since it has been an excellent experience and we have nothing but praise for Mr Dasgupta. His enthusiasm for mathematics is infectious, and admirable is the amount of energy and thought he puts into each lesson. He covers 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). Recently Sam received a book award from the UKMT and got invited to masterclass sessions also organised by the UKMT. Mr Dasgupta’s tutoring was crucial for these achievements. We think Cheenta is rendering an excellent service to humanity by identifying young mathematical minds and nurturing them towards becoming inspired mathematicians of the future.

Jayanta Majumdar

Father of Sambuddha Majumdar, Glasgow, Scotland

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.”

Father of Akshaj Kadaveru, Virginia, USA

## In the coming week..

#### Euler's totient function

Euler’s Totient function gives the reduced residue class for a number. It has beautiful properties including multiplicative (group homomorphism). We explore it in a seminar.

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#### Geometry of varingon

Varingon quadrilaterals are actually parallelograms. They exhibit deep connection between area and midpoint. We explore it in our Math Olympiad Group.

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#### Fun with group theory

Characteristic subgroups are super invariants of a group in some sense. Commutator subgroup is one example of characteristic subgroup. We explore its properties in a seminar.

## Ratio with the sum of digits

Understand the problemFind the 3-digit number whose ratio with the sum of its digits is minimal.Albania TST 2013 Number Theory, Inequalities. Easy Problem Solving Strategies by Arthur Engel Start with hintsDo you really need a hint? Try it first!Suppose that the...

## Does there exist a Magic Rectangle?

Magic Squares are infamous; so famous that even the number of letters on its Wikipedia Page is more than that of Mathematics itself. People hardly talk about Magic Rectangles. Ya, Magic Rectangles! Have you heard of it? No, right? Not me either! So, I set off to...

## Coincident Nine-point Circles

Understand the problemLet be a triangle, its circumcenter, its centroid, and its orthocenter. Denote by , and the centers of the circles circumscribed about the triangles , and , respectively. Prove that the triangle is congruent to the triangle and that the...

## Rational maps to irrational and vice versa?: TIFR 2019 GS Part B, Problem 1

It is an analysis question on functions. It was asked in TIFR 2019 GS admission paper.

## An inequality with unit coefficients

Understand the problemLet be positive real numbers. Show that there exist such that:Iberoamerican olympiad 2011InequalitiesEasyInequalities: An Approach Through Problems by B.J. VenkatachalaStart with hintsDo you really need a hint? Try it first!Try using...

## Expected expectation:TIFR 2019 GS Part A, Problem 20

It is an statistics question on the probability and expectation. It was asked in TIFR 2019 GS admission paper.

## An integer with perfect square digits

Understand the problemFind all positive integers that have 4 digits, all of them perfect squares, and such that is divisible by 2, 3, 5 and 7. Centroamerican olympiad 2016 Number theory Easy An Excursion in Mathematics Start with hintsDo you really need a hint? Try...

## Euler’s theorem and an inequality

Understand the problemLet be the circumcenter and be the centroid of a triangle . If and are the circumcenter and incenter of the triangle, respectively,prove thatBalkan MO 1996 Geometry Easy Let $latex I$ be the incentre. Euler's theorem says that \$latex...

## Functions on differential equation:TIFR 2019 GS Part A, Problem 19

It is an analysis question on the differential equation. It was asked in TIFR 2019 GS admission paper.

## A trigonometric relation and its implication

Understand the problemProve that a triangle is right-angled if and only ifVietnam National Mathematical Olympiad 1981TrigonometryMediumChallenge and Thrill of Pre-college MathematicsStart with hintsDo you really need a hint? Try it first!Familiarity with the...