RMO 2009

Join Trial or Access Free Resources

In this post, there are problems from Regional Mathematics Olympiad, RMO 2009. Try out these problems.

  1. Let $ABC$ be a triangle in which $AB = AC$ and let $I$ be its in-centre. Suppose $BC = AB + AI$. Find $∠BAC$.
    Discussion
  2. Show that there is no integer a such that $ a^2-3a-19 $ is divisible by 289.
  3. Show that $ 3^{4008}+4^{2009} $ can be written as product of two positive integers each of which is larger than $ 2009^{182} $.
  4. Find the sum of all $3$-digit natural numbers which contain at least one odd digit and at least one even digit.
  5. A convex polygon $\Gamma $ is such that the distance between any two vertices of $ \Gamma $ does not exceed 1.
    • Prove that the distance between any two points on the boundary of $ \Gamma $ does not exceed $1$.
    • If X and Y are two distinct points inside $ \Gamma $, prove that there exists a point Z on the boundary of $ \Gamma $ such that $ XZ+YZ \le 1 $.
  6. In a book with page numbers from $1$ to $100$, some pages are torn off. The sum of the numbers on the remaining pages is $4949$. How many pages are torn off?

Some Useful Links:

RMO 2002 Problem 2 – Fermat’s Last Theorem as a guessing tool– Video

Our Math Olympiad Program

More Posts
A Major Milestone in Young Research: Aaditya Punatar and Muskan Sadana Publish in JEI

A Major Milestone in Young Research: Aaditya Punatar and Muskan Sadana Publish in JEI

October 11, 2026

Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]

Read More
Prishaa Shrimali Named Grand Finalist at Regeneron ISEF 2026 for Quantum-Powered Urban Planning Research

Prishaa Shrimali Named Grand Finalist at Regeneron ISEF 2026 for Quantum-Powered Urban Planning Research

October 6, 2026

Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]

Read More
ISI M.Stat Entrance Success Story 2026

ISI M.Stat Entrance Success Story 2026

June 27, 2026

In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance

Read More
ISI B.Stat-B.Math and CMI BSc. Math Entrance Success Story 2026

ISI B.Stat-B.Math and CMI BSc. Math Entrance Success Story 2026

In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]

Read More

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

One comment on “RMO 2009”

© 2010 - 2025, Cheenta Academy. All rights reserved.
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram