Let's discuss a problem based on Integer Sided Obtuse angled triangles with Perimeter. Find the number of integer-sided isosceles obtuse-angled triangles with perimeter 2008. (Indian RMO 2008) Discussion: Let the three sides be a, a and b. Hence 2a + b = 2008 ... (i) Using the triangular inequality we have 2a > b ...(ii) […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2008. Try out these problems. Let $ABC$ be an acute-angled triangle, let $D$, $F$ be the mid-points of $BC, AB$ respectively. Let the perpendicular from $F$ to $AC$ and the perpendicular at $B$ to $BC$ meet in $N$. Prove that $ND$ is equal to […]
A square sheet of paper ABCD is so folded that B falls on the mid-point of M of CD. Prove that the crease will divide BC in the ratio 5:3. Discussion: Assuming the side of the square is 's'. Let a part of the crease be 'x' (hence the remaining part is 's-x'). We apply […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2012. Try them and share your solution in the comments. Problem 1 Let ABCD be a quadrilateral inscribed in a circle. Suppose AB =$latex \sqrt {2 + \sqrt {2} } $ and AB subtends 1350 at the center of the circle. Find the maximum possible […]
This post contains problem from Indian National Mathematics Olympiad, INMO 2011. Try them out and share your solution in the comments. Let D, E, F be points on the sides BC, CA, AB respectively of a triangle ABC such that BD = CE = AF and ∠BDF = ∠CED = ∠AFE. Prove that ABC […]
This a problem from from National Board for Higher Mathematics (NBHM) 2013 based on Cyclic Group Problem for M.Sc Students. Which of the following statements are true? Every group of order 11 is cyclic. Every group of order 111 is cyclic. Every group of order 1111 is cyclic. Discussion: Every group of order 11 is […]
Find all triples $latex (p, x, y) $ such that $latex p^x = y^4 + 4 $, where $latex p $ is a prime and $latex x, y $ are natural numbers. Hint 1: p cannot be 2. For if p is 2 then $latex p^x $ is even which implies $latex y^4 + 4 […]
This post contains Indian National Mathematical Olympiad, INMO 2010 questions. Try to solve these problems and share it in the comments. Let ABC be a triangle with circum-circle $ \Gamma $.Let M be a point in the interior of the triangle ABC which is also on the bisector of $ \angle A $. Let AM, […]
This post contains the problems from Indian National Mathematics Olympiad, INMO 2009 Question Paper. Do try to find their solutions. Indian National Mathematics Olympiad (INMO) 2009 Question Paper: Let ABC be a triangle and P be a interior point such that $ \angle BPC $=$ 90^0 $, $ \angle BAP $ = $ \angle BCP […]
This is a problem from the ISI MStat 2017 Entrance Examination and tests how good are your skills in modelling a life testing experiment using exponential distribution.
This is a problem from the ISI MStat Entrance Examination,2019 involving the MLE of the population size and investigating its unbiasedness.
This is a problem from ISI MStat 2017 PSB Problem 3, where we use the basics of Bijection principle and Vandermone's identity to solve this problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2017 based on Time & Work. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on balls. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Sets and Integers. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Ratio and Inequalities.
Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression. You may use sequential hints to solve the problem.
This problem is an easy application of the basic algorithmic ideas to approach a combinatorics problem using permutation and combination and basic counting principles. Enjoy this problem 3 from ISI MStat 2018 PSB.