Olympiad Prep

Preparação para Olimpíadas de Matemática

Challenge yourself with competition-level problems. Develop creative problem-solving skills and learn elegant proof techniques for national and international math olympiads.

Overall Progress0/155 (0%)

The first problem is a good place to start.

Sample Problems

Topics covered

Number Theory· Teoria dos Números65Combinatorics· Combinatória55Geometry· Geometria27Inequalities· Desigualdades16Logic· Lógica15Algebra· Álgebra12Proofs· Demonstrações10

45 items

0/6

Clever Counting

Contagem Inteligente

Easy

Combinatorics · Combinatória

How many 3-digit numbers can be formed using the digits $\{1, 2, 3, 4, 5\}$ if repetition is allowed?

Sum of the Primes Below 20

Soma dos Primos Menores que 20

Easy

Number Theory · Teoria dos Números

What is the sum of all prime numbers less than 20?

Pattern Recognition

Reconhecimento de Padrões

Easy

Combinatorics · Combinatória

Find the last digit of $7^{2024}$ .

Logic Puzzle

Puzzle Lógico

Easy

Proofs · Demonstrações

Alice, Bob, and Carlos each hold a different number from $\{1, 2, 3\}$ . Alice says: 'My number is 1.' Bob says: 'My number is 2.' Carlos says: 'My number is not 1.' If exactly one of them is lying, who is the liar and what are their numbers?

Triangle Inequality

Desigualdade Triangular

Easy

Proofs · Demonstrações

Can a triangle have sides of lengths 3, 7, and 11? Justify your answer.

Sum of Series

Soma de Série

Easy

Number Theory · Teoria dos Números

Find the sum $1 + 2 + 3 + \ldots + 100$ .