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India Math Olympiad Math Olympiad PRMO Regional Mathematics Olympiads

Indian Olympiad Qualifier in Mathematics – IOQM

Due to COVID 19 Pandemic, the Maths Olympiad stages in India has changed. Here is the announcement published by HBCSE:

Important Announcement [Updated:14-Sept-2020]

The national Olympiad programme in mathematics culminating in the International Mathematical Olympiad (IMO) 2021 and European Girls’ Mathematical Olympiad (EGMO) 2022 has been disrupted by the COVID -19 pandemic in the country. In view of the prevailing situation, the following decisions are announced.

❖ In a departure from the usual four-stage procedure for the selection of the teams to represent India at the IMO 2021 and EGMO 2022 that has been followed in previous years, the selection procedure for the 2020-2021 cycle has been condensed to a three-stage process as an exception only for this year. The three stages will be:

1. A three-hour examination called the Indian Olympiad Qualifier in Mathematics (IOQM) organised by the Mathematics Teachers’ Association (India) (MTA(I)).
2. The Indian National Mathematical Olympiad (INMO) organised by the Homi Bhabha Centre for Science Education – Tata Institute of Fundamental Research (HBCSE – TIFR).
3. The International Mathematical Olympiad Training Camp (IMOTC) organised by HBCSE.

❖ The IOQM will have 30 questions with each question having an integer answer in the range 00-99. The syllabus and standard of this examination will be the same as that of PRMO of previous years.

❖ The INMO will be a four-hour examination with 6 questions. The syllabus and standard of this examination will be the same as that of the INMO of previous years.

❖ The IOQM will be conducted by the MTA(I) with support from Indian Association of Physics Teachers (IAPT) and HBCSE.

❖ The INMO and the subsequent stages of the Olympiad programme will be carried out by HBCSE.

❖ Online enrolment for IOQM is expected to start on the IAPT website (iaptexam.in) by October 15, 2020. Further confirmation regarding this and detailed information regarding eligibility and enrolment for IOQM will be announced shortly. These are expected to be similar to previous years.

❖ The tentative schedule for IOQM is Sunday, January 17, 2021 from 9:00 – 12:00 hrs.

❖ The tentative schedule for INMO is Sunday, March 7, 2021 from 12:00 – 16:00 hrs.

❖ Please note that the schedules are tentative, and are subject to change at short notice, depending on the prevailing pandemic situation in the country.

❖ There will not be any examination equivalent to the Regional Mathematical Olympiad for the 2020-2021 cycle. The detailed criteria for qualification from IOQM to INMO and from INMO to IMOTC will be announced soon.

❖ The programme for stages beyond INMO will be announced at an appropriate later time.

HBCSE

Important Links


Apply for Indian Olympiad Qualifier in Mathematics – IOQM: iaptexam.in

Categories
Opportunity Upcoming math opportunities

National Mathematics Talent Contest (NMTC)

The National Mathematics Talent Contest or NMTC is a national-level mathematics contest conducted by the Association of Mathematics Teachers of India (AMTI).

Aim of the contest:

To find and encourage students who have the ability for original and creative thinking, preparedness to tackle unknown and non-routine problems having a general mathematical ability suitable to their level.

Who can take the test?

The contest is for students of different levels. Here is the breakdown for the same:

1PrimaryGauss ContestV and VI Standards
2Sub JuniorKaprekar ContestVII and VIII Standards
3JuniorBhaskara ContestIX and X Standards
4InterRamanujan ContestXI and XII Standards

The contest is available in English, Gujarati, Hindi, Kannada, Malayalam, Marathi, Tamil or Telugu medium.

Exam fee:

  • Rs. 75/- per candidate (out of which Rs.15/- only will be retained by the institution for all expenses and Rs.60/- per candidate to be sent to AMTI.)
  • The amount paid once is not refundable on any account.

Syllabus

The syllabus of the National Mathematics Talent Contest (NMTC) is similar to the syllabus of the Mathematics Oympiad (Regional, National and International level). It includes:

  • Algebra
  • Geometry
  • Number theory
  • Graph theory & combinatorics

Important Dates:

The dates for this year’s contest is yet to be announced. However, it is certain that the exam is going to be held before the end of 2020 on a Saturday/ Sunday 2020.

Books required to prepare for NMTC:

Since the exam require preparation for Maths Olympiad level, you can click on this link and get all the books necessary for NMTC.

For more information about the exam, you may visit the official website: http://www.amtionline.com/nmtc.php

How to Prepare for NMTC?

The students are encouraged to practice non-routine problems, asked in exams like PRMO, RMO, INMO and IMO.

Cheenta is teaching outstanding kids for Math Olympiads from 4 continents since 10 years now. So, we got the expertise and we want you to utilize it for your benefit.

You can contact us and know more about our course work by filling up a form here: https://www.cheenta.com/contact-us/.

See you!

Categories
Teachers for Tomorrow

Bose Olympiad Senior – Resources

Bose Olympiad Senior is suitable for kids in Grade 8 and above. There are two levels of this olympiad:

  • Prelims
  • Mains

Curriculum

  • Number Theory
  • Combinatorics
  • Algebra
    • Polynomials
    • Complex Numbers
    • Inequality
  • Geometry

Number Theory

The following topics in number theory are useful for the Senior round:

  • Bezout’s Theorem and Euclidean Algorithm
  • Theory of congruence
  • Number Theoretic Functions
  • Theorems of Fermat, Euler, and Wilson
  • Pythagorean TriplesChinese Remainder Theorem

Here is an example of a Number Theory problem that may appear in Seinor Bose Olympiad:

Suppose $a, b, c$ are the side lengths of an integer sided right-angled triangle such that $GCD(a, b, c) = 1$. If $c$ is the length of the hypotenuse, then what is the largest value of the $GCD (b, c)$?

Key idea: Pythagorean Triples

Geometry

The following topics in geometry are useful for the Senior Bose Olympiad round:

  • Synthetic geometry of triangles, circles
  • Barycentric Coordinates
  • Miquel Point Configuration
  • Translation
  • Rotation
  • Screw Similarity

Here is an example of a geometry problem that may appear in the Senior Bose Olympiad:

Suppose the river Basumoti is 25 meters wide and its banks are parallel straight lines. Sudip’s house 10 meters away from the bank of Basumoti. Apu’s house is on the other side of the river, 15 meter away from the bank. If you are allowed to construct a bridge perpendicular to the banks of Basumoti, what is the shortest distance from Sudip to Apu’s house.

Key idea: Reflection

Algebra

The following topics in Algebra are useful for Intermediate Bose Olympiad:

  • Screw similarity, Cyclotomic Polynomials using Complex Numbers
  • AM, GM, and Cauchy Schwarz Inequality
  • Rational Root Theorem, Remainder Theorem
  • Roots of a polynomial

Here is an example of an algebra problem that may appear in Senior Bose Olympiad:

The following sum is greater than which integer: $$ \frac{2}{3} + \frac{3}{4} \cdots + \frac{2019}{2020} + \frac{2020}{2} $$

(A) $2019$ (B) $2020$ (C) $2021$ (D) $2022$

Key idea: inequality

Reference Books

  • Elementary Number Theory by David Burton
  • Principles and Techniques in Combinatorics by Chen Chuan Chong and Koh Khee Meng
  • Polynomials by Barbeau
  • Secrets in Inequalities by Pham Kim Hung
  • Complex Numbers from A to Z by Titu Andreescu
  • Challenges and Thrills of Pre College Mathematics
  • Lines and Curves by Vasiliyev (something else) 
  • Geometric Transformation by Yaglom
  • Notes by Yufei Zhao
  • Trigonometric Delights by El Maor
  • Trigonometry by S.L. Loney
  • 101 Problems in Trigonometry by Titu Andreescu
Categories
Teachers for Tomorrow

Bose Olympiad Intermediate – Resources

Bose Olympiad Intermediate is suitable for kids in Grade 5, 6, and 7. There are two levels of this olympiad:

  • Prelims
  • Mains

Curriculum

  • Elementary Number Theory
  • Counting Principles
  • Algebra
  • Geometry

Number Theory

The following topics in number theory are useful for the Intermediate round:

  • Primes and Composites
  • Arithmetic of Remainders
  • Divisibility
  • Number Theoretic Functions

Here is an example of a Number Theory problem that may appear in Bose Olympiad:

How many positive integer solutions are there of the equation $x^3 – y^3 = 121$ ?

Key idea: Primes

Geometry

The following topics in geometry are useful for the Intermediate round:

  • Locus problems
  • Geometry of lines (angles, parallels)
  • Geometry of triangles (centroid, circumcenter, orthocenter)
  • Geometry of circles (tangents, chords, cyclic quadrilaterals)
  • Conic sections (ellipse, parabola, hyperbola).
  • Triangular Inequality

Here is an example of an geometry problem that may appear in Bose Olympiad:

There are two trees A and B on a field such that distance between A and B is 5 meter. Ayesha is continuously running on the field such that sum of her distances from A and B is always 5 meters. How many times does she visit the midpoint of A and B?

Key idea: Locus

Algebra

The following topics in Algebra are useful for Intermediate Bose Olympiad:

  • Factorization
  • Linear equations
  • Quadratic Equations
  • Inequality

Here is an example of an algebra problem that may appear in Bose Olympiad:

Consider all rectangles of perimeter 40 cm. What is the largest area that can be enclosed by any such rectangle?

Key idea: inequality

Reference Books

  • Mathematical Circles by Fomin
  • Lines and Curves by Vasiliyev
  • Challenges and Thrills of Pre College Mathematics
Categories
Teachers for Tomorrow

Bose Olympiad Junior – Resources

Bose Olympiad Junior is suitable for kids in Grade 1, 2, 3 and 4. There are two levels of this olympiad:

  • Prelims
  • Mains

Curriculum

  • Arithmetic
  • Geometry
  • Mathematical Puzzles

Arithmetic

Basic skills of addition, subtraction and multiplication and division will be sufficient for attending arithmetic problems. Fundamental ideas about place-value system and ratios could be useful for Mains level.

Here is an example of an arithmetic problem that may appear in Bose Olympiad:

Suppose Ajit has 35 cheese sticks. Ajit makes Red Packs containing 3 sticks in each packet. Then Ajit makes Green packs containing 3 Red Packs each. Finally he makes Blue packs, each containing 3 Green Packs. How many unpacked sticks are there at the end of this process?

Key idea: Place Value System

Geometry

A basic understanding is of shapes like triangle, circle, square is sufficient for prelims. Locus (path traced out by a moving point) is another key geometry topic that may appear. At the Mains level, the student may need notions of Area and Perimeter.

Here is an example of an geometry problem that may appear in Bose Olympiad:

Ayesha is running on a field such that his distances from two trees A and B are always equal. That is the distance of the position of Manoj from tree A is equal to the distance of the position of Manoj from tree B at any point of time. Then what is the shape of the path along which Ayesha is running?

Key idea: Locus

Mathematical Puzzles

Mathematical puzzles may involve parallel channels, back tracking, greedy algorithm and recursive logic.

Here is an example of an puzzle problem that may appear in Bose Olympiad:

2019248 teams are playing in a knockout galactic football tournament. In this tournament no match ends in a draw and if you lose a match then you are out of the tournament. In the first round of the tournament the teams are paired up. In each subsequent round if even number of teams remain then they are again paired up, if odd number of teams remain then the highest scoring team is allowed to rest and directly go to the next round. How many matches are played in this tournament?

Key idea: one on one correspondence

Reference Books

  • Mathematics can be fun by Perelman
  • Mathematical Circles for 3 to 8
  • Lines and Curves by Vasiliyev
  • Puzzles by Martin Gardner

Categories
I.S.I. and C.M.I. Entrance

How to use Vectors and Carpet Theorem in Geometry 1?

Here is a video solution for a Problem based on using Vectors and Carpet Theorem in Geometry 1? This problem is helpful for Math Olympiad, ISI & CMI Entrance, and other math contests. Watch and Learn!

Here goes the question…

Given ABCD is a quadrilateral and P and Q are 2 points on AB and CD respectively, such that AP/AB = CQ/CD. Show that: in the figure below, the area of the green part = the white part.

Vectors and Carpet Theorem

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Some Useful Links:

Related Program

Categories
I.S.I. and C.M.I. Entrance

Mahalanobis National Statistics Competition

Mahalanobis National Statistics Competition = MNStatC

organized by Cheenta Statistics Department

with exciting cash prizes.

What is MNStatC?

Mahalanobis National Statistics Competition (MNStatC) is a national level statistics competition, aimed at undergraduate students as well as masters, Ph.D. students, and data analytics, and ML professionals. MNStatC plans to test your core mathematics, probability, and statistics (theoretical + applied) skills.

MNStatC aims

  • to engage the data lovers to explore the beauty of data through effective problem-solving.
  • to enhance the mathematics, probability, and statistics skills for data analytics and machine learning professionals and equip them for the interviews.
  • to let the undergraduate, masters, and Ph.D. students to taste a flavor of out of the box statistics using the same knowledge they learned in their colleges.
  • to build a community and team of authentic and serious data lovers, who plan to change the world through their data-driven minds.
  • to raise awareness of the importance of core statistics, probability, and mathematics in the rising field of Data Science, ML, and AI.

Exam Date and Time

The Exam will be live on 15th November 2020 and end on 30th November.

You can give the exam and enjoy the problems at your own time.

Registration Time and Fee

The Registration will be over by 10th November 2020.

The Registration Fee is Rs 101 for undergraduate students.

The Registration Fee is Rs 241 for masters, Ph.D. students, and data analytics, and ML professionals.

Syllabus

The syllabus is the undergraduate statistics syllabus of a statistics course at an Indian University/College.

Mathematics

  • High School Mathematics (10+2 Level)
  • One Variable Calculus
  • Multiple Variable Calculus
  • Linear Algebra

Probability

(Reference: Mathematical Statistics and Data Analysis by John.A.Rice Chapters 1- 6)
  • Probability Space
  • Conditional Probability, Independence, Bayes Theorem
  • Random Variables, Moments, MGF, Characteristic Function
  • Distribution Function, Density
  • Discrete, Continuous, and Mixed Random Variables
  • Various Probability Distributions and their relationships
  • Joint, Marginal and Conditional Distributions
  • Functions of Joint Distributions
  • Order Statistics and Sampling Distributions
  • Expectation and Variance (advanced)
  • Limit Theorems

Statistics

(Reference: Mathematical Statistics and Data Analysis by John.A.Rice Chapters 7 – 14)
  • Parametric Estimation Theory*
  • Basic Non-Parametric Estimation Theory
  • Testing of Hypothesis*
  • Simple and Multiple Linear Regression*
  • Analysis of Variance*
  • Basic Categorical Data Analysis
  • Basic Bayesian Inference

* = important

Programming Skills

Skill in any mathematical/statistical computational software is a plus. You must take the help of your coding skills to quickly compute stuff.

Competition Pattern

You have to solve a total of 18 multiple choice and numerical problems in 2 hours.

  • Mathematics (3 problems)
  • Probability Theory (6 problems)
  • Theoretical Statistics (6 problems)
  • Applied Statistics (3 problems)

You can take the help of any book or resources or person during the competition.

Exciting Cash Prizes and Discussion Session

1. Undergraduate Students (current position)

1st Cash Prize: Rs 1000

2nd Cash Prize: Rs 400

3rd Cash Prize: Rs 200

2. Masters, Ph.D. students, and Data Analytics Professionals (current position)

1st Cash Prize: Rs 1200

2nd Cash Prize: Rs 600

3rd Cash Prize: Rs 400

Terms and Conditions Apply* (read at the bottom of the page)

There will be a free discussion session for all the candidates with the top few difficult and interesting problems for the competition.

Demo Competition

(Follow the steps)

Download this app in your ios/google play store

Alternatively, you can log in via this web app on pc/laptop.

Login via Google only

Go to Mahalanobis National Statistics Competition.

You will find a Demo Competition over there.

Click on it and enjoy the demo problems.

Your Support

Join the support group in WhatsApp to help you answer your queries.

All the best!

See you soon in the beautiful problems.

Register now

Terms and Conditions Apply*

During prize collection, if you cannot share the proper proof of your college id card or office id card with your name in the application, we will be moving on to the next deserving candidate for the prize.

This is to stop the insurgence of various intelligent scam applicants.

Example: Suppose, you are not an undergraduate and you decide to enroll in the undergraduate exam and you become first in the undergraduate category. We will ask for proof that you are an undergraduate. If you are an undergraduate passout, you belong to the masters’ group. If you cannot provide the proof, we will give the cash prize to the next candidate.

Categories
Teachers for Tomorrow

Letter to parents: talk about infinity

Dear parent,

One of the key contributions of modern mathematics is its tryst with infinity. As parents and teachers we can initiate thought provoking communication with our children using infinity.

Consider the following set:

N = {1, 2, 3, … }

Notice that N contains infinitely many elements.

Take a subset of N that consists of multiples of 2. Lets call it $N_1$.

$N_1= \{2, 4, 6, …\}$

Notice again that N1 contains infinitey many elements. Next consider a subset of N1 that contains only the multiples of 3. Lets call that N2.

$N_2= \{6, 12, 18, 24, … \}$

Student may say: Isn’t 9 a multiple of 3? Should it not be in $N_2$?

No. Because we are taking those multiples of 3 which are in $N_1$. Hence they must be simultaneously multiples of 2 and 3.

Proceeding like this we can create infinitely many sets: $N, N_1, N_2, N_3, …$
These sets are nested! That is $N$ contains $N_1$ contains $N_2$ contains $N_3$ etc. Moreover each of them contains infinitely many terms.

QUESTION: What is in the intersection of all of these sets? That is : what is common in all of them?

This question provokes the child to really think about infinity. For the finite case it can also make a nice combinatorics problem using method of inclusion and exclusion: how many numbers from 1 to 1000 are multiples of 2 or 3 or both.

In fact this last sentence makes the student worry about the word ‘or’. It is is nice place to introduce exclusive or.

Dr. Ashani Dasgupta

Founder, Cheenta

(Ph.D. in Mathematics from University of Wisconsin, Milwaukee, USA. Research Interest: Geometric Group Theory)

Categories
I.S.I. and C.M.I. Entrance

Carpet Strategy in Geometry | Watch and Learn

Here is a video solution for a Problem based on Carpet Strategy in Geometry. This problem is helpful for Math Olympiad, ISI & CMI Entrance, and other math contests. Watch and Learn!

Here goes the question…

Suppose ABCD is a square and X is a point on BC such that AX and DX are joined to form a triangle AXD. Similarly, there is a point Y on AB such that DY and CY are joined to form the triangle DYC. Compare the area of the triangles to the area of the square.

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Some Useful Links:

Related Program

Categories
I.S.I. and C.M.I. Entrance

Bijection Principle Problem | ISI Entrance TOMATO Obj 22

Here is a video solution for a Problem based on Bijection Principle. This is an Objective question 22 from TOMATO for ISI Entrance. Watch and Learn!

Here goes the question…

Given that: x+y+z=10, where x, y and z are natural numbers. How many such solutions are possible for this equation?

We will recommend you to try the problem yourself.

Done?

Let’s see the solution in the video below:

Some Useful Links:

Related Program

Categories
Math Olympiad PRMO

Triangle Problem | PRMO-2018 | Problem No-24

Try this beautiful Trigonometry Problem based on Triangle from PRMO -2018, Problem 24.

Triangle Problem – PRMO 2018- Problem 24


If $\mathrm{N}$ is the number of triangles of different shapes (i.e. not similar) whose angles are all integers (in degrees), what is $\mathrm{N} / 100$ ?

,

  • \(15\)
  • \(22\)
  • \(27\)
  • \(32\)
  • \(37\)

Key Concepts


Trigonometry

Triangle

Integer

Suggested Book | Source | Answer


Suggested Reading

Pre College Mathematics

Source of the problem

Prmo-2018, Problem-24

Check the answer here, but try the problem first

\(27\)

Try with Hints


First Hint

Given that $\mathrm{N}$ is the number of triangles of different shapes. Therefore the different shapes of triangle the angles will be change . at first we have to find out the posssible orders of the angles that the shape of the triangle will be different…

Now can you finish the problem?

Second Hint

case 1 : when $ x \geq 1$ & $y \geq 3 \geq 1$
$$
x+y+z=180
$$
$={ }^{179} \mathrm{C}_{2}=15931$
Case 2 : When two angles are same
$$
2 x+y=180
$$
1,1,178
2,2,176
$\vdots$
89,89,2

Solution

But we have one case $60^{\circ}, 60^{\circ}, 60^{\circ}$
$$
\text { Total }=89-1=88
$$
Such type of triangle $=3(88)$
When 3 angles are same $=1(60,60,60)$
So all distinct angles’s triangles
$$
\begin{array}{l}
=15931-(3 \times 88)-1 \
\neq 3 ! \
=2611
\end{array}
$$
Now, distinct triangle $=2611+88+1$
$
=2700 \
N=2700 \
\frac{N}{100}=27 \
$

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