The simplest example of power mean inequality is the arithmetic mean - geometric mean inequality. Learn in this self-learning module for math olympiad
The simplest example of power mean inequality is the arithmetic mean - geometric mean inequality. Learn in this self-learning module for math olympiad
Gauss trick can be used to solve tricky algebra problems. Learn it in this self-learning module for ISI Entrance and math olympiad
Bijection principle is an important tool in combinatorics. This problem from I.S.I Entrance is useful for Math Olympiad. Try video, sequential hints and practice problems.
Prime numbers are related with polynomials. This problem from I.S.I Entrance is useful for Math Olympiad. Try video, sequential hints and practice problems.
In mathematics, the Gromov boundary of a δ-hyperbolic space (especially a hyperbolic group) is an abstract concept generalizing the boundary sphere of hyperbolic space. Conceptually, the Gromov boundary is the set of all points at infinity. For instance, the Gromov boundary of the real line is two points, corresponding to positive and negative infinity. Suppose X is any set. It is, Suppose, we have […]
Try this beautiful problem of complex number in which we have to find range of the value of a variable so that the relation is valid. Let's solve and use hints if required.
Try this beautiful problem of quadratic equation in which we have to find range of the roots. Let's solve and use hints if required.
Try this beautiful problem of Coordinate Geometry particularly from Nature of curve fromB.Stat. (Hons.) Admission Test 2005. You may use sequential hints to help you solve the problem.
The simplest example of power mean inequality is the arithmetic mean - geometric mean inequality. Learn in this self-learning module for math olympiad
The simplest example of power mean inequality is the arithmetic mean - geometric mean inequality. Learn in this self-learning module for math olympiad
Let us learn about Stirling Numbers of First Kind. Watch video and try the problems related to Math Olympiad Combinatorics
Suppose $r\geq 2$ is an integer, and let $m_{1},n_{1},m_{2},n_{2} \cdots ,m_{r},n_{r}$ be $2r$ integers such that$$|m_{i}n_{j}−m_{j}n_{i}|=1$$for any two integers $i$ and $j$ satisfying $1\leq i <j <r$. Determine the maximum possible value of $r$. Solution: Let us consider the case for $r =2$. Then $|m_{1}n_{2} - m_{2}n_{1}| =1$.......(1) Let us take $m_{1} =1, n_{2} =1, m_{2} =0, n_{1} =0$. Then, clearly the condition holds for $r =2$. […]
This is a work in progress. Please come back soon for more updates. We are adding problems, solutions and discussions on INMO (Indian National Math Olympiad 2021) INMO 2021, Problem 1 Suppose $r \geq 2$ is an integer, and let $m_{1}, n_{1}, m_{2}, n_{2}, \cdots, m_{r}, n_{r}$ be $2 r$ integers such that $$|m_{i} n_{j}-m_{j} […]
Suppose we have a triangle $ABC$. Let us extend the sides $BA$ and $BC$. We will draw the incircle of this triangle. How to draw the incircle? Here is the construction. Draw any two angle bisectors, say of angle $A$ and angle $B$ Mark the intersection point $I$. Drop a perpendicular line from I to […]
In 2021, Cheenta is proud to introduce 5-days-a-week problem solving sessions for Math Olympiad and ISI Entrance.
This post contains problems from Indian National Mathematics Olympiad, INMO 2015. Try them and share your solution in the comments. INMO 2015, Problem 1 Let $A B C$ be a right-angled triangle with $\angle B=90^{\circ} .$ Let $B D$ be the altitude from $B$ on to $A C .$ Let $P, Q$ and $I$ be […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2012 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2012 Set A, Problem 1: Rama was asked by her teacher to […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2013 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2013 Set A, Problem 1: What is the smallest positive integer $k$ […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2015 Set B problems and solutions. You may find some solutions with hints too. PRMO 2015 Set B, Problem 1: A man walks a certain distance and rides back in $3 \frac{3}{4}$ hours; he could ride both ways in $2 \frac{1}{2}$ hours. How many […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2014 problems and solutions. You may find some solutions with hints too. PRMO 2014, Problem 1: A natural number $k$ is such that $k^{2}<2014<(k+1)^{2}$. What is the largest prime factor of $k ?$ PRMO 2014, Problem 2: The first term of a sequence is […]