Connections

How it works

Imagine you are given a grid that has been partially filled with Xs and Os like the one below:

Your goal is to add Xs and Os so the grid is completely filled, but there are some rules you have to follow:

  • All the Xs must be in one connected region and all the Os must be in one connected region
    • All the Xs are in one connected region if it is possible to get from any X to any other X only going up, down, left, or right (not diagonally), and not passing through any squares with Os (and similarly for Os). For example, in the grid below, all the Xs are in one connected region, but the Os are not:
  • There can't be any 2 x 2 squares within the grid that are all Xs or all Os, like in the grid below:

Can you figure out how to fill the grid above with Xs and Os without breaking the rules? Can you do it without guessing?

In this activity, students explore a variety of different puzzles. They start with puzzles involving 3 x 3 grids, then move on to puzzles on larger grids. Along the way, the puzzles get more challenging, and students encounter some puzzles that are impossible!

Puzzles handout

Why we like this activity

  • It’s fun! Students enjoy trying to solve the puzzles.

  • It helps students to develop logical reasoning.

  • It requires students to engage in mathematical habits of mind:

    • Finding and using strategies to solve the puzzles efficiently (without guessing)

    • Using logic and understanding and explaining when trying to determine which puzzles are impossible

  • It has a low floor and a high ceiling: Students can start solving puzzles by trial and error, but as the puzzles get more challenging, more careful strategizing is required!

 
 

This activity was adapted from the Julia Robinson Mathematics Festival's activity Yin-Yang.