Try this problem from RMO 2015 from Chennai Region based on Integer Solution of Polynomial. Problem: Integer Solution of Polynomial Solve the equation $latex y^3 + 3y^2 + 3y = x^3 + 5x^2 - 19x + 20 &s=2 $ for positive integers x, y. Discussion: $latex y^3 + 3y^2 + 3y = x^3 + 5x^2 […]
This is a problem from RMO 2015 Mumbai Region based on inequality. Problem: RMO 2015 Mumbai Region Let x, y, z be real numbers such that $ x^2 + y^2 + z^2 - 2xyz = 1 $ and $ s=2$ . Prove that $ (1+x)(1+y)(1+z) \le 4 + 4xyz $ and $ s=2$ Discussion Note […]
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 […]
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Right Rectangular Prism.
This is a problem from ISI MStat 2016 sample paper which tests the student's ability to write a model and then test the equality of parameters in it using appropriate statistics.
Try this beautiful problem from Geometry: Sectors in Circle from AMC-10A, 2012. You may use sequential hints to solve the problem
Try this beautiful problem from Algebra: Sum of whole numbers from AMC-10A, 2012. 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 Pyramid with Square base.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Repeatedly Flipping a Fair Coin.
Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Smallest positive Integer.