Find the number of 8 digit numbers sum of whose digits is 4. Discussion: Suppose the number is $latex a_1 a_2 a_3 ... a_8 $.The possible values of $latex a_1 $ are 1, 2, 3, 4. We consider these four cases. If $latex a_1 = 4 $ then all other digits are 0 (since sum […]
In this post, there are questions from Regional Math Olympiad 2013. Try out the problems. Find the number of 8 digit numbers sum of whose digits are 4.Discussion Find the number of 4-tuples (a,b,c,d) of natural numbers with $latex a \le b \le c $ and $latex a! + b! + c! = 3^d […]
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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 […]
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. 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 Rationals.
Try this beautiful problem from Algebra, based on Sum of digits from AMC-10A, 2020. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on Integer from AMC-10A, 2020. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Average and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and Roots. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Row of Pascal Triangle.