Rebuild
How it works
Rebuild is a solitaire card game. There are 4 spaces, and you start with a pile of 4 playing cards, Ace through 4, on top of one of the spaces. The pile is in sorted order with the Ace on top and the 4 on the bottom. Your goal is to rebuild the pile (in the same sorted order) on one of the other spaces. When moving cards, there are some rules you must follow:
- You can only move one card at a time
- You can only move a card if it is on top of a pile
- You can put a card on an empty space, but you can never put a bigger card on top of a smaller card
Can you figure out how to rebuild the pile on a different space while following these rules? What if there are 5 cards? 6 cards? What if there are only 3 spaces instead of 4 spaces?
In this activity, students explore a variety of different challenges with different numbers of cards and different numbers of spaces. They try to determine which of these challenges are possible and which are impossible, and for the challenges that are possible, they try to find the minimum number of moves required to solve the challenge.
Why we like this acivity
- It’s fun! Students enjoy trying to solve the different challenges.
- It helps students to develop algorithmic reasoning.
It requires students to engage in mathematical habits of mind:
- Using logic and finding and using strategies to solve the challenges
- It has a low floor and a high ceiling: It's easy for students to start exploring by trial and error, but as the challenges get more difficult, more careful strategizing is necessary!
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.