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Truth Tellers and Liars
In Chapter 8, we're introduced to Mome Raths and Slithy Toves. If you're curious, Lewis Carroll (real name Charles Dodgson) was frequently asked how to pronounce the nonsense words in the poem "Jabberbocky". According to Carroll, "Mome Raths" should be pronounced so it rhymes with "bath" (be sure to use a British accent).
In "Math and Magic in Wonderland", both creatures look the same, but Mome Raths always tell the truth and Slithy Toves always lie. Here, L explains how to tell them apart:
The kids did really well telling Mome Raths from Slithy Toves (with a little assistance) and the puppets made it extra fun. It's a pretty advanced skill to be able to grasp negatives (lies) and think through multiple scenarios. As a bonus, "Slithy Tove" is now part of our vocabulary. The other day, I heard L tell E not to be a Slithy Tove when she was dishonest about something!
The classic logic problem of "Truth Tellers and Liars" is not only a great brain puzzle, but also an introduction to Boolean algebra. In Boolean algebra, named after English mathematician George Boole in 1847, all variables are either TRUE or FALSE. Since electrical circuits have two states as well (on and off), Boolean logic is a basis for all computers. In this video, I explain how to make a truth table:
Your Turn to Play:
- Learn more about solving Truth-Tellers and Liars Problems (along with little quizzes to test your skills)
- Check out BBC's tutorial on Boolean Algebra.
- Mark your calendar for November 2nd (George Boole's birthday) when Math Circles Ireland will be providing a course for kids on Boolean algebra. You can find out more and download a sample of activities here: Boole2School
- Logic Lab is a free online simulation which lets you try out different logic gates.
- Try this Boolean Logic Card Game
The first case that the girls are asked to assist with involves finding a fake coin from a group of nine coins. They accomplish this using a balance scale (and only two weighings!). My own twins had a fun time making their own balance scales (with mixed results). Here's E explaining how the balance scale was used to find the fake coin in the story:
Your Turn to Play:
- Test out your logic skills in Out of Balance (a free online game from smart-kit.com) or Seesaw Logic (a free online game from mathplayground.com).
- This Balance Beans logic game looks like a lot of fun, too!
- Try Balance - it's similar to Sudoku, where you have to place each number once on the game board, but you have to get the numbers to "balance"
- Try to find the minimum number of weighings required to find a lighter coin among 12 coins? 15 coins? 30 coins?
Here is the Book Club / Math Circle schedule (you can join any time):
Week of August 1st:
- Book Club Kick-Off Party!
- Read Chapter 1: Mrs. Magpie's Manual
- Memorizing digits of Pi
- Calculating your age on other planets
- Read Chapter 2: Magic Square
- Making tangrams
- Acute, obtuse, and right angles
- Magic squares
- Adding consecutive numbers using Gauss's trick
- Read Chapter 3: Secret Codes
- Word permutations
- Cartesian coordinates
- Operations on odd and even numbers
- Read Chapter 4: Rabbit Trails
- Drawing a perfect circle
- Making a compass
- Finding the center of a circle
- Exploring Pi
- Famous mathematicians who followed rabbit trails
- Read Chapter 5: Two Worlds Join
- Mobius strips
- Read Chapter 6: River Crossing
- River Crossing Problems
- Build a boat and explore buoyancy
- Read Chapter 7: Seven Bridges
- Seven Bridges of Königsberg problem
- The power of exponents
- Word ladders
- Thales's method for calculating the height of an object
- Read Chapter 8: Veracity
- Truth-tellers and liars
- Finding a fake coin using a balance scale
- Archimedes buoyancy principle
- Read Chapter 9: To Catch a Thief
- John Napier's Rooster
- Doubling pennies and calculating exponents
- Towers of Hannoi
- Read Chapter 10: The Vorpal Sword
- Square numbers
- Prime numbers
- Fibonacci Sequence
- Relativity and time dilation
- Acrostic poems
- Read Chapter 11: Two Great Powers
- Book Club Finishing Party with Prizes!
Thanks for joining us. I can't wait to read your comments!