This page features training materials and preparation tips for the Global Logic and Reasoning Competition.

Preparation Tips for Participants

Below, you will find a set of tips designed to help you prepare for the Global Logic and Reasoning Competition. These recommendations are tailored to support your success in the competition and enhance your skills:

1. Know the Competition Format
   Start by understanding the structure and requirements of each round: the Qualification Round focuses on diverse topics across all branches of logic and reasoning, the Semi-Final Round includes reading comprehension tasks based on research literature, and the Final Round tests quick problem-solving under time pressure. Reviewing past GLRC problems will help you grasp the diversity and difficulty level of each round.


2. Focus on the Core Topics
   The problems in GLRC come from a range of reasoning areas, including deductive logic, probabilistic reasoning, causal reasoning, critical reading, modeling and estimation, and strategic reasoning. Make sure you are comfortable with the fundamental concepts, inference rules, and key tools in these topics to build a solid foundation for tackling problems.


3. Train Your Problem-Solving Skills
   Work on improving your creativity, reasoning, and analytical thinking by solving logic and reasoning problems from textbooks, past competitions, and the resources recommended below. Practice formalizing arguments, computing probabilities, identifying assumptions, and recognizing patterns. These skills will help you approach even the most challenging GLRC problems effectively.


4. Learn from Mistakes
   Reflecting on your mistakes and learning from them is an essential part of growth in any competition. First, try to solve the problems as far as possible. Then, compare them to a given solution and evaluate at which steps you made mistakes and correct them accordingly.


5. Use the Available Resources
   Take advantage of past GLRC problem sets, recommended textbooks, and online platforms to sharpen your skills. Additionally, the GLRC team is available to provide assistance and guidance; do not hesitate to contact us for support.


6. Prepare for Reading Comprehension (Semi-Final Round)
   The Semi-Final Round often features problems inspired by research articles. Practice reading and summarizing texts, focusing on extracting relevant data, understanding the structure of the argument, and connecting findings to broader reasoning concepts. Reading articles that present arguments and evidence will help develop this skill.


7. Simulate Timed Problem-Solving (Final Round)
   Time management is essential for the Semi-Final and even more the Final Round. Practice solving problems within set time limits to develop a sense of pacing.


8. Collaborate and Learn from Others
   Join study groups, reasoning clubs, or connect with GLRC Ambassadors to discuss strategies and share insights. Collaboration can help you explore new problem-solving approaches and stay motivated throughout your preparation.


9. Enjoy the Learning Experience
   Keep in mind that GLRC prioritizes learning and expanding your knowledge while participating. Engage with each problem, and treat every challenge as an opportunity to deepen your understanding of how we think, argue, and solve problems.

Syllabus

The following outlines the core reasoning domains covered in GLRC, along with key concepts and tools that are fundamental to each area. This syllabus is not comprehensive, but it covers much of the ground you will encounter. Most problems do not require specific subject knowledge; instead, they test general reasoning ability. Keep in mind that subsequent rounds build on the concepts of previous rounds, so the ideas below carry forward as the competition progresses.

• Deductive Reasoning & Logic:
  Deductive reasoning establishes the foundational principles that govern valid inference. This includes understanding propositional and predicate logic, truth values, and the structure of valid arguments. Mastery of these concepts is essential for distinguishing sound conclusions from invalid ones and for understanding more advanced topics.
  • Logical Connectives: Conjunction, disjunction, negation, implication, biconditional
  • Valid Argument Forms: Modus ponens, modus tollens, hypothetical syllogism
  • Truth Tables: Evaluating compound statements over all truth assignments
  • Implication: \(p \rightarrow q \equiv \neg p \lor q\) (Material conditional)
  • Contrapositive: \(p \rightarrow q \equiv \neg q \rightarrow \neg p\) (Logically equivalent forms)


• Probabilistic Reasoning:
  Reasoning under uncertainty is central to sound decision-making. This includes understanding probability, conditional probability, and how to update beliefs when new evidence arrives. These concepts allow you to weigh likelihoods and avoid common statistical mistakes.
  • Conditional Probability: \(P(A \mid B) = \frac{P(A \cap B)}{P(B)}\)
  • Bayes' Theorem: \(P(A \mid B) = \frac{P(B \mid A)\,P(A)}{P(B)}\) (Updating beliefs with evidence)
  • Independence: \(P(A \cap B) = P(A)\,P(B)\) (When events do not influence each other)
  • Expected Value: \(E[X] = \sum_i x_i\,P(x_i)\) (Weighted average of outcomes)
  • Complement Rule: \(P(\neg A) = 1 - P(A)\)


• Causal Reasoning:
  Causal reasoning deals with distinguishing causation from correlation and identifying the factors that genuinely produce an effect. Understanding confounders, controls, and counterfactuals helps explain why outcomes occur and how to evaluate claims about cause and effect.
  • Correlation vs. Causation: Recognizing that association does not imply a causal link
  • Confounding Variables: Hidden factors that influence both cause and effect
  • Counterfactuals: Asking what would have happened without the cause
  • Controlled Comparison: Isolating one variable while holding others constant
  • Necessary vs. Sufficient Causes: Distinguishing required conditions from triggering ones


• Strategic & Game Reasoning:
  Strategic reasoning deals with decisions where outcomes depend on the choices of others. Understanding payoffs, equilibria, and optimal strategies is essential for applications ranging from negotiation to competition and cooperative problem-solving.
  • Payoff Matrices: Representing outcomes for combinations of choices
  • Dominant Strategy: A choice that is best regardless of what others do
  • Nash Equilibrium: No player can gain by unilaterally changing strategy
  • Zero-Sum vs. Non-Zero-Sum: Whether one player's gain is another's loss
  • Backward Induction: Reasoning from the end of a sequence back to the start


• Critical Reading & Argument Analysis:
  Critical reading is the study of how arguments are constructed and how to evaluate them. Understanding premises, conclusions, assumptions, and logical fallacies helps explain how a text persuades and how to assess whether its reasoning holds.
  • Argument Structure: Identifying premises, conclusions, and intermediate steps
  • Hidden Assumptions: Unstated premises that an argument depends on
  • Logical Fallacies: Ad hominem, straw man, false dilemma, circular reasoning
  • Strengthening and Weakening: Identifying evidence that supports or undermines a claim
  • Inference vs. Assumption: Distinguishing what follows from what is taken for granted


• Modeling & Estimation:
  Modeling and estimation is about reasoning well when the situation outpaces the available evidence. Often you cannot wait for data: by the time solid studies exist, the world has already moved on (judging the impact of a fast-moving technology is a classic case). The skill is to structure a messy question, decide what actually matters, and reason to a defensible estimate rather than freezing or guessing blindly.
  • Structuring the Problem: Turning a vague, real-world situation into something solvable
  • Choosing Variables: Identifying the few assumptions that actually drive the answer
  • Estimation: Order-of-magnitude and Fermi-style reasoning to a workable number
  • Simplification: Cutting detail without breaking what matters
  • Bounding Uncertainty: Reasoning under uncertainty and stating how confident you are

Additionally, the Semi-Final Round usually includes research problems, which require you to read a research article. The Final Round can also include questions related to the previous problems (e.g., the research article) from the Semi-Final Round and Qualification Round. Consider checking out this page to understand better how GLRC differs from other competition formats and what to expect:

• About GLRC (How GLRC differs from other competitions and what to expect.)

Book Recommendations

Most introductory logic, probability, and critical thinking textbooks are useful and contain the information required to approach the problems. For reference, please have a look at the following list of recommended books:

• Logic & Deductive Reasoning:
• Patrick Hurley and Lori Watson. A Concise Introduction to Logic. Cengage Learning.
• Irving Copi, Carl Cohen, and Victor Rodych. Introduction to Logic. Routledge.
• Wilfrid Hodges. Logic. Penguin Books.
• Graham Priest. Logic: A Very Short Introduction. Oxford University Press.


• Critical Thinking & Argumentation:
• Richard Paul and Linda Elder. Critical Thinking: Tools for Taking Charge of Your Learning and Your Life. Pearson.
• Anthony Weston. A Rulebook for Arguments. Hackett Publishing.
• M. Neil Browne and Stuart Keeley. Asking the Right Questions: A Guide to Critical Thinking. Pearson.
• Stella Cottrell. Critical Thinking Skills: Developing Effective Analysis and Argument. Palgrave Macmillan.
• Douglas Walton. Informal Logic: A Pragmatic Approach. Cambridge University Press.


• Probabilistic & Statistical Reasoning:
• Sheldon Ross. A First Course in Probability. Pearson.
• Ian Hacking. An Introduction to Probability and Inductive Logic. Cambridge University Press.
• Daniel Kahneman. Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Darrell Huff. How to Lie with Statistics. W.W. Norton.


• Problem-Solving, Modeling & Estimation:
• George Polya. How to Solve It. Princeton University Press.
• Sanjoy Mahajan. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. MIT Press.
• Douglas Hubbard. How to Measure Anything: Finding the Value of Intangibles in Business. Wiley.
• Martin Gardner. The Colossal Book of Short Puzzles and Problems. W.W. Norton.


• Strategic & Game Reasoning:
• Avinash Dixit and Barry Nalebuff. The Art of Strategy. W.W. Norton.
• Ken Binmore. Game Theory: A Very Short Introduction. Oxford University Press.
• William Poundstone. Prisoner's Dilemma. Anchor Books.