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

1. Let be a triangle in which and let be its in-centre. Suppose . Find .
Discussion
2. Show that there is no integer a such that is divisible by 289.
3. Show that can be written as product of two positive integers each of which is larger than .
4. Find the sum of all -digit natural numbers which contain at least one odd digit and at least one even digit.
5. A convex polygon is such that the distance between any two vertices of does not exceed 1.
• Prove that the distance between any two points on the boundary of does not exceed .
• If X and Y are two distinct points inside , prove that there exists a point Z on the boundary of such that .
6. In a book with page numbers from to , some pages are torn off. The sum of the numbers on the remaining pages is . How many pages are torn off?

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

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

1. Let be a triangle in which and let be its in-centre. Suppose . Find .
Discussion
2. Show that there is no integer a such that is divisible by 289.
3. Show that can be written as product of two positive integers each of which is larger than .
4. Find the sum of all -digit natural numbers which contain at least one odd digit and at least one even digit.
5. A convex polygon is such that the distance between any two vertices of does not exceed 1.
• Prove that the distance between any two points on the boundary of does not exceed .
• If X and Y are two distinct points inside , prove that there exists a point Z on the boundary of such that .
6. In a book with page numbers from to , some pages are torn off. The sum of the numbers on the remaining pages is . How many pages are torn off?

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

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### One comment on “RMO 2009”

1. neelanjan mondal says:

Please tell me the solutions of the problems 5,rmo-2009

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