## Linear Towers of Hanoi

This is a classical variation over the Towers of Hanoi where some moves are forbidden. Specifically, disks cannot move directly between the left-most and the right-most pegs. The middle peg must be involved in every moves.

Beside of that extra complexity, the problem remains unchanged: you are requested to move the whole stack of disks from one extremity peg to the other one. You can only move one disk at a time, and a bigger disk cannot be placed over a smaller one.

As with the classical version, it is much easier to produce a recursive solution, and you are absolutely able to devise this solution if you think hard enough about it.

The standard recursive algorithm for classical Hanoi is of complexity 2^n-1 where the standard recursive algorithm for this variation is of complexity 3^n-1.
The standard recursive algorithm for classical Hanoi involves two recursive calls sandwiching one movement of the largest disk, the standard recursive algorithm for Linear Hanoi involves three recursive calls sandwiched around two movements of the same disk.