"How do I involve my child in challenging mathematics? He gets good marks in school tests but I think he is smarter than school curriculum." "My daughter is in 4th grade. What competitions in mathematics and science can she participate in? How do I help her to perform well in those competitions?" "I have a […]
What is RMO? RMO or Regional Math Olympiad is the second round of Mathematics Contest in India after the Pre-regional Mathematics Olympiad (Pre-RMO or PRMO) leading to the prestigious International Mathematics Olympiad (IMO). It is held in the month of December (the first Sunday of December). The test is conducted in each of the 19 […]
Problem: Let ABCDE be a regular pentagon inscribed in a circle. P be any point in the minor arc AE. Prove that PA + PC + PE = PB + PD Proof: Suppose length of each side is 's' and each diagonal is 'x'. Apply Ptolemy's Theorem in PABC. We have PA . s + […]
In this post, here are problems from Regional Mathematics Olympiad, RMO 2011 Re-Test Paper. Let ABC be an acute angled scalene triangle with circumcenter O and orthocenter H. If M is the midpoint of BC, then show that AO and HM intersect at the circumcircle of ABC. Let n be a positive integer such […]
Let $ABC$ be a triangle. Let $D, E, F$ be points respectively on the segments $BC, CA, AB$ such that $AD, BE, CF$ concur at the point $K$. Suppose $\frac{BD}{DC} = \frac{BF}{FA}$ and $∠ADB = ∠AFC$. Prove that $∠ ABE = ∠ CAD$. Let $ (a_1a_2a_3.....a_{2011}) $ be a permutation (that is arrangement) of the […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2010. Try out these problems. Let $ABCDEF$ be a convex hexagon in which the diagonals $AD, BE, CF$ are concurrent at $O$. Suppose the area of triangle $OAF$ is the geometric mean of those of $OAB$ and $OEF$; and the area of the triangle […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2009. Try out these problems. Let $ABC$ be a triangle in which $AB = AC$ and let $I$ be its in-centre. Suppose $BC = AB + AI$. Find $∠BAC$.Discussion Show that there is no integer a such that $ a^2-3a-19 $ is divisible by […]
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 […]
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.