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Brilliant

Logic

via Brilliant

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Overview

The beginning of our introductory math journey is Logic. Through these challenging problem solving exercises, you'll construct the critical thinking skills that are the basis for mathematical reasoning.

You'll use limited information to make predictions – eliminating the impossible to uncover the truth. This course builds up to some truly mind-bending challenges!
By the end of this course, you'll be able to spot logical fallacies, navigate some strategic game theory, understand machine logic, and use the symbolic languages of logic to understand fun riddles.

Syllabus

  • Introduction: Put your logic to the test with these warmups!
    • Order Logic: Solve problems by visualizing relationships.
    • Abstract Order Logic: There's often more than one way to solve a problem.
    • Strategic Order Logic: Stretch the information you're given as far as you can.
  • Puzzles and Riddles: Eliminate the impossible and uncover the truth!
    • Truth Seeking: Find out who is telling the truth and who is lying.
    • Worst Cases: Solve problems by considering the worst case scenario.
    • Shuffles: Where did everything get shuffled to?
    • False Information: Sometimes the information you're given is not reliable.
    • Process of Elimination: Keep track of the extremes and contradictions.
  • Multi-Level Thinking: Even trickier puzzles and the tools you need to solve them.
    • I Don't Know: Can you gain information from ignorance?
    • Hat Puzzles: Can you figure out who can figure out the color of their hat?
    • Hat Colors with Strategy: Now there are more hats and more people.
    • Headlights: Exactly how much can you learn from no one knowing anything?
    • Machines Learning Chess: Make sure you never make the same mistake twice.
  • The Rational Detective:
    • Androids: Can you get a lying android to tell you the truth?
    • Extrapolate: What happens when you try to apply logic to a crowd?
    • Unknown Answers: Compare answers to see if you can unpack the truth.
    • Jokers: Some people just want to watch the logical world burn.
    • Rebellion: Solve the logic puzzles, save the world.

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