This is a problem from RMO 2015 from Mumbai Region based on Cyclic Quadrilaterals and Incenters. Problem: RMO 2015 Mumbai Region Let ABC be a right angled triangle with $ \angle B = 90^0 $ and $ s=2 $ and let BD be the altitude from B on to AC. Draw $ DE \perp AB […]
This is a problem from Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on Polynomial with positive integers. Try to solve it. Site title Title Primary category Separator Problem: Let P(x) be a polynomial whose coefficients are positive integers. If P(n) divides P(P(n) -2015) for every natural number n, prove that P(-2015) = 0. Discussion: Let […]
This is a problem from the Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on the Number of Three-digit numbers. Try to solve it. Problem: Number of Three-digit numbers Determine the number of 3 digit numbers in base 10 having at least one 5 and at most one 3. Discussion: (Suggested by Shuborno Das in […]
This is a problem from the Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on Diagonal of a Quadrilateral. Try to solve it. Problem: Diagonal of a Quadrilateral Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose $ a^2 + b^2 + c^2 […]
This is a problem from Regional Mathematics Olympiad, RMO 2015 Chennai Region based on the Minimal value problem. Try to solve it. Problem: Minimal value problem Find the minimum value of $ \displaystyle { \frac{ ( x + \frac{1}{x} )^6 - ( x^6 + \frac{1}{x^6}) - 2}{(x+\frac{1}{x})^3 + (x^3 + \frac{1}{x^3} )} } $ and […]
This is a problem from the Regional Mathematics Olympiad, RMO 2015 Chennai Region based on a List of numbers. Problem: From the list of natural numbers 1, 2, 3, … suppose we remove all multiples of 7, all multiples of 11 and all multiples of 13. At which position in the resulting list does the number […]
This is a Rectangle Problem from RMO (Regional Mathematics Olympiad) 2015 from Chennai Region. Problem: Rectangle problem from RMO 2015 Two circles $latex \Sigma_1 &s=2 $ and $latex \Sigma_2 &s=2 $ having centers at $latex C_1 &s=2 $ and $latex C_2 &s=2 $ intersect at A and B. Let P be a point on the […]
This post contains RMO 2015 Problems and solutions from Chennai Region. Find the minimum value of $ \displaystyle { \frac{ ( x + \frac{1}{x} )^6 - ( x^6 + \frac{1}{x^6}) - 2}{(x+\frac{1}{x})^3 + (x^3 + \frac{1}{x^3} )} } $ and $ s=2$ and $ x \in \mathbb{R} $ and $ s=2 $ and $ x […]
This post contains Regional Mathematics Olympiad, RMO 2015 Mumbai Region problems, and solutions Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose $ a^2 + b^2 + c^2 + d^2 = ab + bc + cd + da $ and the area of […]
The second stage examination of INMO, the Regional Mathematical Olympiad (RMO) is a three hour examination with six problems. The problems under each topic involve high level of difficulty and sophistication. West Bengal RMO 2015 Problem 6 Solution has been written for RMO preparation series. The book, Challenge and Thrill of Pre-College Mathematics is very […]