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Brilliant

Joy of Problem Solving

via Brilliant

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Overview

Problem solving requires creativity, intuition, knowledge, and skill. It also requires practice.

This course dives deep into four mathematical explorations, each of which quickly goes beyond 'rote' learning, challenging you to explore patterns and create proofs. You'll get a mental workout that strengthens your problem solving abilities, especially in logic and algebra.
This course can be enjoyed by any and everyone interested in solving beautiful, kinesthetic arrangement puzzles and delightful problems in logic and algebra. By the end of this course, you'll become a much stronger mathematical thinker!

Syllabus

  • Intro to Problem Solving: Apply creativity, lateral thinking, and mathematical skill.
    • Logical Reasoning: Warm up with these logic puzzles, ranging from simple to mind-bending!
    • Geometric Shortcuts: See how a clever perspective is often the key to geometric problem solving.
    • Flipping Pairs: Detangle the possible from the impossible in these interactive puzzles.
  • Truth Tellers and Liars: Deduce fact from fiction given assumptions and observations.
    • This Sentence Is True: Reason out when these statements are true and when they're false.
    • If It Starts With If, Then...: Explore the peculiar behavior of "If...then..." statements.
    • Jokers & Other Tricksters: See what happens to logic when a "trickster" can either tell the truth or lie...
    • Humans & Vampires: Wrangle each of the characters in this sequence into one of four crazy categories.
    • Incomplete Information: You can stretch a little information a long way if you're careful and clever in your reasoning.
  • Operator Searches: Solve problems in reverse using the rules of arithmetic!
    • Strategies for + and -: You have only two options for each box: plus or minus.
    • Use Only + and -: What are all of the possible results of these equations using only plus and minus?
    • Concatenation Strategies: Concatenation lets you push two digits together to make a two-digit number.
    • Concatenation, +, and -: Strategically combine addition, subtraction, and concatenation together.
    • 123456789=100: How can addition, subtraction, and contenation be interwoven to make this expression equal 100?
    • Possible vs. Impossible: Figure out which operations work, or prove that the goal is impossible!
  • Coin Rearrangements: Can you slide, jump, and flip to transform one pattern into another?
    • Coin Warmups: Pause a moment to think carefully and then rearrange these coins from one configuration to another.
    • Sliding Puzzles: The strategies for solving these challenges get a bit more complex.
    • Sliding and Jumping Part 1: In this game, not only can the coins slide, they can jump!
    • Sliding and Jumping Part 2: In this version of the sliding and jumping and game, things get more restricted...
    • Sliding and Jumping Part 3: Is it still possible to win this game in each of these strange cases?
    • Coin Solitaire Part 1: In this last coin game, removing one coin from a line-up flips over its neighbors.
    • Coin Solitaire Part 2: Explore coin solitaire systematically and prove a beautiful, mathematical result!
  • Matchstick Puzzles: These spatial puzzles are math problems in disguise!
    • Lateral Thinking Matchstick Puzzles: Combine all of the strategies you've seen to solve this last set of challenges.
    • Overlapping Figures: Stretch your intuition to new, creative perspectives.
    • Mastering Matches Moving: Strategically move around these matchsticks to create overlapping shapes.
    • Removing Matchsticks: Push your matchstick moving skills to the limit!
    • No Squares!: In these challenges, you're restricted to removing matchsticks instead of moving them.
    • Mastering Matchstick Removals: What does it take to get rid of all of the squares in these matchstick patterns?
    • Strategy Summary: What patterns can you make adding matchsticks one at a time to these figures?

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