Knaves and Knights


Source: OpenClipart.com

Type: Investigation

Theme: Logic

Grades: 6, 7, 8, 9, 10, 11, 12

Learning Target: Students will reason mathematically by creating a Knights and Knaves logic puzzle through truth table construction.

Instructions

Example:

Everyone on Smullyan's Island is either a knight or a knave. Knights always tell the truth. Knaves always lie, but their looks won't help you distinguish the two.

You meet two people, person A and person B. You want to know if either of them are knights? You ask them, "Which one of you are a knight?"

Person A replies, "At least one of us is a knave." Who are they?

The truth table below will help you solve this riddle.

knights and knaves truth table

This project is for individuals.

  1. Research Knights and Knaves puzzles.
  2. Create a truth table that represents your puzzle. Middle school students can re-write an existing Knights and Knaves or Portia puzzle, creating a truth table for it. Use your own characters and situations.
  3. Provide your puzzle to a minimum of three students. They should check their solution with a truth table. 
  4. Collect data on your puzzle. Was your puzzle too difficult, too easy, or just right?

Submission

  1. Puzzle text using proper grammar and dialogue punctuation conventions.
  2. Truth Table that demonstrates logic and solution to the puzzle
  3. Data collected for your puzzle.

Resources

Exit Ticket
CCSS Math Practice
  • I can make sense of problems and persevere in solving them.
  • I can reason abstractly and quantitatively.
NGSS Crosscutting Concepts
  • Cause and Effect
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Samples