Color Scheme
How it works
Imagine that we have 5 chips arranged in a line. Each chip is red on one side and blue on the other, and they are arranged so they alternate red, blue, red, blue, red. Our goal is to get all the chips to be the same color (either all red or all blue). However, there are some specific rules we have to follow:
- You can only turn over chips in pairs (2 at a time)
- You can only turn over a pair of chips if they are next to each other
Given these rules, is it possible to get all the chips to be red? Is it possible to get all the chips to be blue? What about for different arrangements of chips with the red and blue chips in a different order, or with different numbers of red and blue chips?
In this activity, students explore a variety of different arrangements of chips, starting with 5 chips, then moving on to 6, 7, and 8 chips. They discover that for some arrangements, it's possible to get all the chips to be red, and for others, it's impossible (and likewise for blue), and they see if they can figure out a way to predict when it will be possible and when it will be impossible.
Why we like this activity
It’s fun! Students enjoy trying to get all the chips to be the same color.
It helps students to develop algorithmic reasoning.
It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to solve the challenges
Using logic and understanding and explaining when trying to determine which challenges are impossible
Looking for patterns and making and testing predictions when trying to predict whether or not a challenge is possible
It has a low floor and a high ceiling: Students can start solving challenges by trial and error, but predicting which challenges will be possible and which will be impossible requires more careful thinking!
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.