Let's solve the Regional Mathematics Olympiad Problem, RMO 2017 from Goa and Maharashtra. Try the problems and check your solutions here. (\ 1).((\ 16) marks)Consider a chessboard of size (\ 8) units(\ \times8) units (i.e., each small square on the board has a side length of (\ 1) unit).Let (\ S) be the set of […]
Here are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions. Looking for just the problems? Download the PDF here. RMO 2017, Problem 1: Let AOB be a given angle less than \( 180^o \) and let P be an interior point of […]
Let's discuss a problem based on Ceva's Theorem from Regional Mathematics Olympiad, RMO, 2002, Problem 1. Watch, learn and enjoy.
How many positive integers less than \(1000\) have the property that the sum of the digits of each such number is divisible by \(7\) and the number itself is divisible by \(3\) ? Suppose \(a,b\) are positive real numbers such that \(a\sqrt{a}+b\sqrt{b}=183\). \(a\sqrt{b}+b\sqrt{a}=182\). Find \(\frac{9}{5}(a+b)\). A contractor has two teams of workers: team A and […]
Here is the post for the Regional Mathematics Olympiad (India) RMO Number Theory Problems. These are problems from previous year papers. (This is a work in progress. More problems will be added soon). RMO Number Theory Problems: Find all triples (p, q, r) of primes such that pq = r + 1 and 2(p 2 […]
Problems Problem 1 Let \( a, b, c \) be positive real numbers such that $$ \frac{a}{1+a} + \frac{b}{1+b} + \frac{c}{1+c} = 1 $$ Prove that \( abc \leq \frac{1}{8} \)