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!
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 […]
Overview of Math Olympiads in United States The American Mathematics Competitions (AMC) are the first of a series of competitions in middle school and high school mathematics that lead to the United States team for the International Mathematical Olympiad (IMO). AMC has three levels: AMC 8 - grade 8 and below AMC 10 - grades 10 and […]
Day 1 - 03 January 2014 1 Let be two positive sequences defined by and for all . Prove that they are converges and find their limits. 2 Given the polynomial where is a positive integer. Prove that can't be written as a product of non-constant polynomials with integer coefficients. 3 Given a regular […]
Problem 1In a triangle $A B C,$ let $D$ be a point on the segment $B C$ such that $A B+B D=A C+C D .$ Suppose that the points $B, C$ and the centroids of triangles $A B D$ and $A C D$ lie on a circle. Prove that $A B=A C .$Solution […]
This is a problem from Indian National Mathematics Olympiad, INMO, 2013 based on Orthocenter on perpendicular bisector. Try out this problem. Problem: Orthocenter on perpendicular bisector In an acute angled triangle ABC with AB < AC the circle $latex \Gamma $ touches AB at B and passes through C intersecting AC again at D. Prove […]
Find the number of 4-tuples (a,b,c,d) of natural numbers with $latex a \le b \le c $ and $latex a! + b! + c! = 3^d $ Discussion: Number of 4-tuples The basic idea is: factorial function is faster than the exponential function in the long run. Note that all three of a, b, c […]
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Negative & Positive Roots. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Calculus. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and Roots. You may use sequential hints.
Try this beautiful Geometry Problem on Equilateral Triangle from AMC-10A, 2010.You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry:cubical box from AMC-10A, 2010. You may use sequential hints to solve the problem
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Graphs in Calculus. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra:Roots of cubic equation from AMC-10A, 2010. You may use sequential hints to solve the problem
This is a problem from ISI MStat Examination 2016. This primarily tests the student's knowledge in finding confidence intervals and using the Central Limit Theorem as an useful approximation tool.
Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.