Lord of the Rings — San Francisco Math Circle

We’re hosting a math festival at San Francisco State on Saturday, March 15! For more info and to register, visit https://sfmathcircle.org/sf-state-math-festival

 
 
 
 
 

Lord of the Rings

How it works

Imagine that we have a set of rings that are all different sizes and a set of pegs. To start, the rings are stacked on the leftmost peg in order from smallest (at the top) to largest (at the bottom).

Our goal is to move all the rings from the leftmost peg to the rightmost peg. When moving the rings, we have to follow two rules:

  • We can only move the top ring from a given peg.
  • We can never put a bigger ring on top of a smaller ring.

Is it possible to get all the rings onto the rightmost peg? If so, how many moves are required? What about for different numbers of rings and pegs?

In this activity, students explore a variety of different puzzles with different numbers of rings and pegs. The puzzles increase in difficulty as rings are added and pegs are removed.

Why we like this activity

  • It’s fun! Students enjoy trying to solve the puzzles.
  • It helps to develop algorithmic reasoning.

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

    • Finding and using strategies to solve different puzzles using as few moves as possible.
    • Making and testing predictions about how many moves will be required to solve different puzzles.
    • Understanding and explaining their strategies and predictions.
  • It has a low floor and a high ceiling: Students can start trying to solve 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.