A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!
A.M.- G.M. Inequality can be used to prove the existence of Euler Number. A fascinating journey from classical inequalities to invention of one of the most important numbers in mathematics!
RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.
RMO 2018 Tamil Nadu Problem 2 Sequential Hints and Solution. A polynomial problem with seasoning from geometric progression.
RMO 2018 Tamil Nadu Problem 1 Sequential Hints and Solution. A beautiful geometry problem that uses properties of cyclic quadrilaterals.
Regional Math Olympiad (Tamil Nadu Region, 2018) Problems, Sequential Hints and Discussion.
The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.
Parity and divisibility are two interesting tools of elementary number theory. Coupled with an estimation with AM-GM inequality, we have excursion into the queen of mathematical disciplines.
This post contains RMO 2018 solutions, problems, and discussions. RMO 2018, Problem 1: Let \(ABC\) be a triangle with integer sides in which \(AB < AC\). Let the tangent to the circumcircle of triangle \(ABC\) at \(A\) intersect the line \(BC\) at \(D\). Suppose \(AD\) is also an integer. Prove that gcd\((AB,AC) >1\). RMO 2018, […]
A convex polygon \( \Gamma \) is such that the distance between any two vertices of \( \Gamma \) does not exceed 1. Prove that the distance between any two points on the boundary of \( \Gamma \) does not exceed 1. If X and Y are two distinct points inside \( \Gamma \), prove that […]
The Problem Let ABC be a triangle in which AB = AC and let I be its in-centre. Suppose BC = AB + AI. Find ∠BAC. Big Ideas For any triangle ABC, \( \frac{\sin A}{a} = \frac{\sin B } {b} = \frac {\sin C }{c} \). Addendo: If \( \frac{a}{b} = \frac{c}{d} \) then each of […]
Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988, Question 14, based on Reflection.
This is a beautiful sample problem from ISI MStat 2018 PSB Problem 1. This is based on finding the real solution of a system of homogeneous equations . We provide detailed solution with prerequisites mentioned explicitly.
Try this beautiful Number Theory problem from PRMO, 2019, problem-18, based on Ordered Pairs. You may use sequential hints to solve the problem.
Try this beautiful Geometry problem from PRMO, 2019, problem-23, based on finding the maximum area. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry based on Rectangle Pattern from AMC-10A, 2016, Problem 10. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Ratio of area of Circles from AMC-10A, 2009, Problem 21. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988, Question 11, based on Complex plane.
Try this I.S.I. B.Stat Entrance Objective Problem from TOMATO based on a derivative of Function. You may use sequential hints to solve the problem.
This is a problem involving BLUE for regression coefficients and MLE of a regression coefficient for a particular case of the regressors.