Puerto Rico Team Selection Test, 2023. Day 2
Problem 5 Six boxes contain apples, bananas, and cucumbers. The number of apples in each...
Puerto Rico Team Selection Test, 2023. Day 1
Problem 1 A palindrome is a positive integer number that remains the same when its...
Team Selection Test for Centro and Ibero 2022
Problem 1 Let us call a natural number interesting if any of its two consecutive...
Puerto Rico Team Selection Test, 2022. Day 2
Problem 4 The six-pointed star is regular with all the interior angles of the $12$...
Puerto Rico Team Selection Test, 2022. Day 1
Problem 1 Find all triples $(a,b,c)$ of positive integers such that: $$a + b +...
Discrete Continuity
Let some quantity $Q(x)$ change its value by $\pm 1$, starting at an integer number...
OMPR 3d Round 2022, High School
Problem 1 How many sets of integers greater than $1$, with two or more elements,...
OMPR 3d Round 2022, Middle School
Problem 1 A subset of $10$ elements of the set $\{1,2,3,…,90\}$ is called Boricua if...
Solutions of Swiss Mathematical Olympiad, 2021
Problem 1 Let $O$ be the center of the circumcircle of an acute triangle $ABC$....
Solutions to the Polish Mathematical Olympiad, 2021
Problem 1 Positive integers $a$, $b$, $n$ satisfy the equality $$ \frac{a}{b} = \frac{a^2+n^2}{b^2+n^2} $$...
Swiss Mathematical Olympiad, 2021
Problem 1 Let $O$ be the center of the circumcircle of an acute triangle $ABC$....
How to Solve Diophantine Equations: Modulus
Diophantine equations are equations that are solved in integer numbers. We can solve some diophantine...
Diophantine Equations: Factorization
Diophantine equations are equations that are solved in integer numbers. We can solve some diophantine...
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...
Selected Problems from Iberoamerican Mathematics Olympiad, 2020
Problem 1 Let $ABC$ be an acute scalene triangle such that $AB <AC$. The midpoints...
Central American and Caribbean Mathematics Olympiad, 2020 Day 2
Day 2 Problem 1 Consider a triangle $ABC$ with $BC>AC$. The circle with...
Central American and Caribbean Mathematics Olympiad, 2020 Day 1
Day 1 Problem 1 A four-digit positive integer is called $virtual$ if it...
Puerto Rico Team Selection Test, 2020
Problem 1 We have $10,000$ identical equilateral triangles. Consider the largest regular hexagon that can...
