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Logic (2020)

via Brilliant

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!
    • Warmup Puzzles: Get started with some logic warmups.
    • Truth-Seeking: Who or what is telling the truth?
    • Strategic Deductions: Stretch the information you're given as far as it can go!
  • The Rational Detective: Eliminate the impossible and uncover the truth!
    • Riddles of Order: What order do these racers finish in?
    • Crafty Counting: Learn strategies for counting that go far beyond just counting.
    • Mystery Containers: What's in each of these mystery boxes?
    • Futoshiki: Arrange the numbers to match the inequalities.
    • Shuffles: Where did everything get shuffled to?
    • False Information: Solve problems where the people giving you hints might be lying.
  • Puzzles and Riddles: Even trickier puzzles and the tools you need to solve them.
    • Werewolves: Who's a werewolf?
    • Logical Language: Explore the logical use of the words "and", "or", and "not".
    • If A, then B.: If you do this quiz, you will learn about sentences like this one.
    • Elimination Grids: Solve classic logic elimination puzzles.
    • Jigsaw Map: Where do the pieces go on the map?
    • Poisoned Chocolate: Don't take the last chocolate!
    • Luk Tsut K'i: Find the complete solution to a classic game.
    • Puppies and Kittens: Solve a fuzzier, livelier variant of the poisoned chocolate game.
    • Poisoned Chocolate II: What happens when the chocolate comes in rectangles?
    • Game Search Algorithms: Learn how simple AI systems approach game strategy.
  • Multi-Level Thinking: If you know that I know that you know... what then?
    • Perfect Information: If everyone follows the same logic, can you find out what they know?
    • Hat Colors: Can you figure out who can figure out the color of their hat?
    • Hat Colors with More People: What happens to hat puzzles when there are more hats and more people?
    • Red-Eyed Dragons: Exactly how much can you learn from no one knowing anything?
    • Logical Pirates: Beware! Every pirate is as logical, greedy, and cutthroat as every other pirate.
    • Knights and Knaves: Solve classic truthteller-liar puzzles where someone else knows the answer.
    • Indirection: Can you trick a liar into telling you the truth?
    • Knights and Knaves En Masse: What happens when you try to do logic at a big island party?
    • Jokers: Solve tricky variants of knights and knaves puzzles where some residents can behave like either.
    • Other Variations: Twist your mind around these unusual variants.
    • Humans and Vampires: Now there are four types of island resident: can you still work out the truth?
    • Challenges: Challenge yourself with our hardest selection of logic puzzles.

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