This post contains problems from Indian National Mathematics Olympiad, INMO 2018. Try them and share your solution in the comments. INMO 2018, Problem 1 Let ABC be a non-equilateral triangle with integer sides. Let D and E be respectively the mid-points BC and C A, let G be the centroid of triangle ABC. Suppose D, […]
The most beautiful equation in mathematics is: It is often attributed to Swiss Mathematician Leonhard Euler. Interestingly enough, this is nothing but a statement about rotation! 23 is a shorthand way of writing 2 × 2 × 2. But this is very very different from what means. Mathematicians use this trick over and over again. They overload notations. In fact is a […]
We have indicated the source of these problems. Do not look up solutions. It is fun to try it yourself or see others try them live! Let P be an interior point of triangle ABC and AP, BP, CP meet the sides BC, CA, AB in D, E, F respectively. Show that \( \frac{AP}{PD}=\frac{AF}{FB}+\frac{AE}{EC} \) […]
Sine of an angle, half chord and vertical projection Note that half chord corresponding to a half arc is same as the magnitude of vertical projection.
Watch the solution of an interesting problem on Triangles on a sphere and learn how to solve it. You may try the problem yourself and then watch the video. PROBLEM Suppose the earth is a perfect sphere. You are on its surface at point A. First, you walk 1 mile south, then 1 mile east […]
You may want to look into the first part
Cheenta Opportunity is an initiative for the benefit of Cheenta Olympiad candidates. We dig up opportunities and resources available all around the world for our students. Here we are exploring UCLA Full Scholarship Program - MUMS. University of California, Los Angles is one of the leading universities in the world. Its mathematics department is held in […]
The central theme of the thousand flowers program is: connected ideas and connected problems. We will illustrate the idea using some examples. But before we do so, let's point out the theoretical motivation behind such a program. It is greatly borrowed from the pedagogical experiments of Rabindranath Thakur. (Reference: https://bn.m.wikisource.org/wiki/বিশ্বভারতী). One of his major criticisms of […]
This is a beautiful problem ISI MStat 2016 (sample) PSB based on order statistics . We provide detailed solution with the prerequisites mentioned explicitly.
Try this beautiful problem from algebra, based on Sum of the digits from AMC-10A, 2007. You may use sequential hints to solve the problem
Try this beautiful problem based on Integers and Divisors from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry:Radius of a circle.AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from Geometry based on medians of triangle from PRMO 2018. You may use sequential hints to solve the problem.
Try this beautiful sum of Co-ordinates based on co-ordinate Geometry from AMC-10A, 2014. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry based on Hexagon from AMC-10A, 2014. You may use sequential hints to solve the problem
This is a beautiful problem from ISI MStat 2016 (sample ) PSB Problem 1. This is based on finding the minimum value of a function subjected to the restriction .
Try this beautiful problem from the Pre-RMO, 2019 based on the Diameter of a circle. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on positive integers from PRMO 2019. You may use sequential hints to solve the problem.