Logic Puzzles Made Visual

When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type:

Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn’t buy an apple or kale. And so on…

Now that the Common Core Standards for Mathematical Practice talk explicitly about problem solving, reasoning, and sense making, the educational benefits of logic puzzles  seem more relevant than ever.

Below (and here) is an interactive Web Sketchpad model for introducing elementary students to logical reasoning. Unlike traditional logic puzzles that come pre-written, these logic puzzles can be created by your students. As an example, start by dragging two statements across the vertical divider line.  Let’s assume you pick “Ann is taller than Bill” and “Bill is taller than Carlos.”

Your job is to change their heights of Ann, Bill, Carlos, and Denise (dragging the points atop their heads) so that both statements are true. Notice that the star turns from red to green when you’ve satisfied both statements simultaneously. You’re now ready to answer a question: Who is taller, Ann or Carlos?

Your diagram likely shows that Ann is taller than Carlos, but is this always true? What I really like about this model is that students can change the heights of Ann, Bill, and Carlos , but as long as Ann is taller than Bill and Bill is taller than Carlos, Ann will always be taller Carlos. I think deducing this conclusion is made easier with the interactive visual model.

By comparison, suppose that students drag the statements “Ann is shorter than Bill” and “Bill is taller than Denise” across the vertical divider. What, if anything, can be said about Ann and Denise? In this case, the students can arrange the heights of the three people so that either Ann or Denise is taller while still keeping the star green.

Here are some additional challenges:

  • Can you pick statements that make it impossible to turn the star green?
  • How many statements can you drag across the vertical divider line and still be able to make the star green?
  • Click the arrow in the bottom-right corner of the model to try a more abstract variation of these logic problems. The names Ann, Bill, Carlos, and Denise are replaced by the letters A, B, C, and D and “shorter than” and “taller than” are replaced by the symbols < and >.

An annotated list of all our elementary-themed blog posts is here.

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