Try this problem from Duke Math Meet 2009 Problem 6 based on Count of Sparse Subsets. This problem was asked in the team round. Call a set S sparse if every pair of distinct elements of S differ by more than 1. Find the number of sparse subsets (possibly empty) of {1, 2, . . […]
This post contains problems from the first relay round of the Duke Math Meet 2009. Try to solve these problems.
Try this problem from Duke Math Meet 2009 Problem 7 based on Area of Ellipse. This problem was asked in the individual round.
This is a problem from Regional Mathematics Olympiad, RMO 2011 Problem 1 based on the angles of a triangle. Try to solve it out!
দৈনন্দিন জীবনে বস্তু গোনবার পদ্ধতি খুব কাজের জিনিস । এই পোস্ট থেকে একটি পদ্ধতি সম্বন্ধে জানব যা ডিরিশিলিটের বাক্স নীতি বা ইংরেজিতে Pigeonhole principle বলে।
This post contains RMO 2007 problems. Try to solve these problems Let ABC be an acute-angled triangle; AD be the bisector of angle BAC with D on BC, and BE be the altitude from B on AC. Show that $ \angle CED > 45^\circ $ . [weightage 17/100] Let a, b, c be three natural […]
Let's understand the factor method of Diophantine equations step-by-step. Aso, try the question related to it. Diophantine Equations Consider an equation for which we seek only integer solutions. There is no standard technique of solving such a problem, though there are some common heuristics that you may apply. A simple example is $ x^2 - […]
Here is an excerpt from an email conversation that I had with one of our student's parent: "While we have lots of books with problems, the one challenge has been that problems in the books are not classified by level of difficulty or arranged in increasing order of difficulty. Much like a weight-lifter gradually increases […]
This is a session plan for 'Mathematics in Summer 2014'. (Venue: Scotland, Glasgow). Let's discuss Homological Triangles. Introduction to homological triangles, perspectivities. Menalaus' Theorem, Desargues Theorem Anti parallel lines, some examples of homological triangles, homothety as a special case of homology, cevian, orthic triangle, some basic properties of angle bisectors' Special Triangles and points: anti-supplemental […]