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 […]
A post on homological triangles... topic of our math camp August 2014 (in Scotland)
a and b are two numbers having the same no. of digits and same sum of digits (=28). Can one be a multiple of the other? a is not equal to b. (courtesy Abhra Abir Kundu) Is $latex e^x-sinx $ a polynomial ? (courtesy Tias Kundu) Find the number of onto function from set A containing […]
This post contains an interesting problem from ISI BMath 2014 based on the jump of a frog and the lotus. Solve and enjoy this problem. Problem: Jump of a frog Problem n (> 1) lotus leafs are arranged in a circle. A frog jumps from a particular leaf by the following rule: It always moves […]
This is a problem from CMI Entrance 2014 based on Map from a power set to n-set. Problem: Map from a power set to n-set (1) Let A = {1, ... , k} and B = {1, ... , n}. Find the number of maps from A to B . (2) Define $latex \mathbf{ P_k […]
This is a problem from Chennai Mathematical Institute, CMI Entrance 2014 based on area of a region. Try to solve it. Problem: Area of a region $latex \mathbf{ A= {(x, y), x^2 + y^2 \le 144 , \sin(2x+3y) le 0 } } $ . Find the area of A. Discussion: $latex \mathbf{ x^2 + y^2 […]
Let $latex \mathbf{ x \in \mathbb{R} , x^{2014} - x^{2004} , x^{2009} - x^{2004} in \mathbb{Z} }$ . Then show that x is an integer. (Hint: First show that x is a rational number)Discussion: $latex \mathbf{ x^{2014} - x^{2004} - x^{2009} + x^{2004} = x^{2014} - x^{2009} = x^{2009}(x^{5} - 1 ) }$ is an […]
This post contains problem from Chennai Mathematics Institute, CMI 2014 B.Sc. Entrance Paper. Try to solve them out. Help us to add and rectify problems and solutions to this paper. We are collecting problems from student feed back. 4 Point Problems Find the minimum value for x for which $latex \mathbf{ 50!/ (24)^n }$ is […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.
Try this beautiful problem from the Pre-RMO, 2017 based on Series Problem. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Trigonometry and positive integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Odd and Even integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Two and Three-digit numbers.
Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.
Try this problem from the Singapore Mathematics Olympiad, SMO, 2010 based on the application of the Pythagoras Theorem. You may use sequential hints.
Try this beautiful problem from Probability in Dice from AMC-10A, 2009. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. You may use sequential hints to solve the problem.