Spot flaws in arguments, identify logical fallacies, and evaluate whether conclusions actually follow from their premises.

Apply set notation (∪, ∩, ⊆, complement) and inclusion-exclusion to solve problems with two and three overlapping sets.

Read the clues and eliminate possibilities until only one valid arrangement remains. These puzzles develop systematic elimination skills.

Solve problems involving ratios, rates, unit rates, scale factors, and proportional relationships in real-world contexts.

Find nth-term formulas, identify arithmetic and geometric sequences, and use algebra to answer questions about any term in a pattern.

Simplify expressions, expand brackets, solve equations and systems, and apply algebra to real-world logic problems.

Calculate probabilities of single and compound events, use conditional probability, and find expected values in real-world situations.

Combine multiple concepts — percentages, averages, proportions, and logic — into problems that require a clear plan before calculating.