Towers of Hanoi


This model represents A simple Towers of Hanoi example with four rings. Wikipedia has a lot of great information on the problem.

This is a great example of difference equations/recursion equations in the real world! The recursion relation is given by \(y(n+1) = 2y(n) + 1\). We use an initial condition of \(y(1)=1\); i.e. if you have only one ring, it takes one step to move the stack to another peg. Then, our solution is given by \(y(n) = 2^n-1\). This means, if we use all 4 rings in this file, it takes \(2^4-1 = 15\) steps at a minimum to move the stack from one tower to the other!

Design process:

I designed this using Fusion 360.