$3$ Towers of Hanoi

Devise a recursive solution for the Disordered Towers of Hanoi problem, where the rings are initially distributed arbitrarily

among the three poles but are, of course, stacked legally on each pole, so that higher rings have smaller diameters. The objective

is to move this mess of rings so that all $n$ rings will be on $B($and in the right order$).$ The rings still have the names $1,2,$dots,$n,$

where ring $1$ is the smallest.

Suggestion: Define

procedure $DTH(n,A,B,C)$

to solve this new problem in a way that is analogous to that for the regular Towers of Hanoi problem. Start with yous previous

standard ToH solution, and use editing to duplicate lines as needed $($or not$),$ and to include the predicate IsIthere$(j,x),$

which is true if pole $x$ contains the ring named $j,$ and is false otherwise. So the code should explain what to do when $x$ is

$A,$ is $B,$ and i $C.$

$3\mathrm{.}1)$ How would a beginner try to solve this problem?

$3\mathrm{.}2)$ What subproblem would the Pro want to solve to progress toward completion?

How would the pro complete the solution after the previous objective was achieved?

$3\mathrm{.}3)$ Now write the code for the three cases to get a complete solution to this problem.