This challenge should only be attempted after students have learned about exponents. Start by explaining the Tower of Hanoi puzzle. Be sure to tell them the goal is to solve the puzzle in as few moves as possible. Have them solve the puzzle with 1, 2, and 3 rings, having the students record their number of moves each time. If the student fails to find the solution involving the minimal number of moves, tell them it can be done in fewer, and have them try again. Once they've found the minimal number for 1, 2, and 3 rings, challenge them to conjecture a formula for \(n\) rings. I got the idea for this challenge from here. There are also some interesting questions here.

Next, give your students this challenge:

Snap by NRICH

Conclude by leading this investigation:

Algebra Exercises

by MathPickle