Puerto Rico Team Selection Test, 2023. Day 2
Problem 5 Six boxes contain apples, bananas, and cucumbers. The number of apples in each...
Team Selection Test for Centro and Ibero 2022
Problem 1 Let us call a natural number interesting if any of its two consecutive...
Solutions of Swiss Mathematical Olympiad, 2021
Problem 1 Let $O$ be the center of the circumcircle of an acute triangle $ABC$....
Swiss Mathematical Olympiad, 2021
Problem 1 Let $O$ be the center of the circumcircle of an acute triangle $ABC$....
Polish Mathematical Olympiad, 2021
Problem 1 Positive integers $a$, $b$, $n$ satisfy the equality $$ \frac{a}{b} = \frac{a^2+n^2}{b^2+n^2} $$...
Team Selection Test for Iberoamerican Math Olympiad 2021
Problem 1 Let $N=2021^2k+2021$, where $k$ is a positive integer. Alfredo calculates the sum of...
Puerto Rico Team Selection Test, 2021. Day 2
Problem 4 How many numbers $\overline{abcd}$ with different digits satisfy the following property: if we...
Puerto Rico Team Selection Test, 2021. Day 1
Problem 1 Ana and Beto are playing a game. Ana writes a whole number on...
Titu’s Lemma
Titu’s Lemma states that for all positive real numbers $x_1$, $x_2$, … , $x_n$ and...
How to Solve Diophantine Equations: Quadratic Formula
Diophantine equations are equations that are solved in integer numbers. We can solve some diophantine...
AMC 8 Preparation (The Book)
AMC 8 Preparation Book presents the most popular methods and techniques that are used to...
Team Selection Process for IMO in Ukraine
The team selection process for IMO in Ukraine consists of 4 rounds of olympiad exams...
Pigeonhole Principle
Let $m,n \in \mathbb{N}$ and $n>m$. The Pigeonhole Principle states that if $n$ items are...