Cryptograms
These fun puzzles will help you develop patterns and tricks to solve algebra problems faster and more skillfully.
In this course, we'll develop the foundational math that touches algebra, probability, and logic — but not by handing you facts to memorize. Math isn't about memorizing formulas, it's about problem solving.
This course covers many traditional logic, algebra, and probability techniques. Each exploration is designed to push your mindset and mathematical skills to the next level! In short: you'll need to think for yourself, think creatively, and think strategically — that's what real problem solving requires.
Explore the foundations of algebra and logic without any rote memorization.
These fun puzzles will help you develop patterns and tricks to solve algebra problems faster and more skillfully.
Figure out what operations are needed in each challenge, or prove that the goal is impossible!
Limber up with some warm-ups, and then give your brain a workout with three tougher challenges.
Divisibility rules, cryptograms, and other digit magic.
Apply the divisibility rules for 1, 2, 5, and 10, and summarize why this set is special.
What's different about the divisibility rules for 4 and 8?
The rules for 3, 6, 7, and 9, are a fair bit stranger than what you've seen so far.
Apply your understanding of divisibility rules to cracking cryptogram puzzles!
Creatively extend your cryptogram solving strategies to handle a different operation.
Each of these challenges will require the skillful and elegant application of logic, number theory, and algebra.
Find the pattern, then make predictions.
Is there order, repetition, or regularity in these visual patterns?
Understand and create recursive and explicit descriptions of patterns.
Find and interpret the algebraic descriptions of patterns.
Use variables to describe interrelated unknowns.
Are these statements provable, or can you think of counterexamples?
Explore and understand this algebraic property using geometric visualizations.
Logic shows you how to win!
Get your analytical and critical thinking skills warmed-up and ready for some strenuous exercise!
Apply logic to determine the secret identities of the entities in each challenge.
Understand the behavior of "If...then..." statements within the framework of formal logic.
Are the small clues in each of these challenges enough information to figure out the whole situation?
Extend your strategic, logical thinking to challenges that require several separate stages of reasoning.
The mathematics of comparisons: ratios, percentages, and fractions.
Learn how to use rewriting fractions as a problem-solving shortcut.
It's easy to answer these rate and speed questions incorrectly if you're not careful!
Use these problems to expose and correct a few common misconceptions about percentages.
Put your intuition for ratios and percentages to the test in some tricky scenarios!
Explore powerful, intuitive shortcuts for comparing the magnitudes of ratios.
Extend your skill using fractions to these challenging, subtle cases where multiple variables are involved.
What are the odds of getting all these problems right?
Strengthen your intuition for probabilistic math by thinking systematically about outcomes.
Learn how to create and use distribution charts to tackle challenging problems.
Learn how and when to switch perspectives and ask, "When does this event NOT happen?".
Use these problems to expose and correct some common misconceptions about probability.
Practice making smart, strategic decisions, even when the outcomes are uncertain.
Analyze lotteries, coin flips, and other games of chance to learn how probability can help you avoid costly mistakes.
Demonstrate what you've learned with these difficult problems.
Break down and tackle difficult problems that require the creative, coordinated use of multiple techniques.
Get ready to first solve these manipulation challenges, and then to prove that your solutions are ideal.
These advanced cryptograms are more difficult than any you've seen in this course so far!
Extend basic arithmetic into surprising, beautiful, and useful patterns.
Dive deeper into exploring the properties of large sums of consecutive numbers.
Review a sample of the major topics covered in this course: algebra, number theory, logic, and probability.