## Blogs about: Olympiad Normal Problem Solving

#### Putnam 2012 Day 2 — 1 comment

: 1. Let be a class of functions from to that satisfies: (i) The functions and are in (ii) If and are … more →

Tags: Problem-solving, contest

#### Putnam 2012 Day 1

: 1. Let be real numbers in the open interval Show that there exist distinct indices such that are the … more →

Tags: Problem-solving, contest

#### Sum of some angles in a polygon — 2 comments

: Let be a convex polygon which has no two sides which are parallel. For each side consider the vertex … more →

#### Nice inequality similar to IMO 2011

: Prove that Note the similarity to the IMO 2011 inequality, and surprisingly the same method works. P … more →

Tags: inequalities, inequality, Trick

#### IMC 2012 Problem 6

: Consider a polynomial Albert Einstein and Homer Simpson are playing the following game. In turn, the … more →

Tags: Combinatorics, IMC, Polynomials

#### IMC 2012 Problem 5

: Let be a rational number and let be a positive integer. Prove that the polynomial is irreducible in … more →

Tags: IMC, Polynomials

#### IMC 2012 Problem 4

: Let be a continuously differentiable function that satisfies for all . Prove that for all . 45.56443 … more →

Tags: Analysis, IMC, functions

#### IMC 2012 Problem 3 — 2 comments

: Given an integer , let be the group of permutation of the numbers . Two players and play the followi … more →

Tags: Algebra., Combinatorics

#### IMC 2012 Problem 2 — 2 comments

: Let be a fixed positive integer. Determine the smallest positive rank of an matrix that has zeros al … more →

Tags: Algebra., IMC

#### IMC 2012 Problem 1

: For every positive integer denote denote the number of ways to express as a sum of positive integer. … more →

Tags: Combinatorics, IMC

#### IMO 1996 Day 1 — 1 comment

: Problem 1 We are given a positive integer and a rectangular board with dimensions . The rectangle is … more →

#### IMO 1995 Day 1

: I decided to test myself on solving some IMO problems. Here are my solutions for IMO 1995 Day 1. Apa … more →

#### Balkan Mathematical Olympiad 2012 Problem 4 — 4 comments

: Let be the set of positive integers. Find all functions such that the following conditions both hold … more →

Tags: functional equation

#### Balkan Mathematical Olympiad 2012 Problem 3

: Let be a positive integer. Let For each subset of , we write for the sum of all elements of , with t … more →

Tags: Algebra.

#### Balkan Mathematical Olympiad 2012 Problem 2

: Prove that for all positive real numbers and . Balkan Mathematical Olympiad 2012 Problem 2 Solution: … more →

Tags: inequalities

#### Balkan Mathematical Olympiad 2012 Problem 1

: Let , and be points lying on a circle with centre . Assume that . Let be the point of intersection o … more →

Tags: Geometry

#### Characterization of a normal matrix — 2 comments

: A matrix with complex entries is called normal if , where is the conjugate transpose of . Prove that … more →

Tags: Higher Algebra, Matrix, adjoint

#### SEEMOUS 2012 Problem 4

: a) Compute . b) Let be an integer. Compute . a) Make the change of variable . The limit becomes Prov … more →

#### There isn't such a function — 2 comments

: Prove that there is no continuous function such that and . Proof: As noted in the first comment, a c … more →

Tags: Analysis, function, Continuous

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