Jumping Stacks
How it works
Imagine that we have 5 cubes arranged in a line. Our goal is to connect the cubes together into a single stack. However, the only way the cubes can move is by jumping on top of each other. There are some specific rules we have to follow when stacking cubes on top of each other:
The distance a stack of cubes jumps is equal to the number of cubes in the stack:
- A single cube jumps 1 space
- A stack of 2 cubes jumps exactly 2 spaces
- A stack of 3 cubes jumps exactly 3 spaces
- Etc.
Cubes or stacks can only jump onto other cubes or stacks, not onto empty spaces
Given these rules, is it possible to connect all 5 cubes into a single stack? What if there are 6 cubes? 7 cubes? 8 cubes? What if the single stack has to end up in a specific position? What if the cubes have to be arranged in a specific order in the single stack?
In this activity, students first try to get the cubes into a single stack without worrying about where the stack ends up or the order of the cubes in the stack before moving on to explore these more complex puzzles.
Why we like this activity
It’s fun! Students enjoy trying to solve the puzzles.
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 puzzles
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 Students can start solving puzzles by trial and error, but as the puzzles get more challenging, more careful strategizing is required!
This activity was developed in collaboration with the Julia Robinson Mathematics Festival and is based on an activity from MathPickle.