This is my solution. I use global variables so I never copy/duplicate the stacks, just pass pointers to which stack I am moving to where. It still recursively calls the move stack function, one less counter each time until it gets to one counter. N.B. I found it really hard work getting this code into the answer box - needed to manually edit the html.

def move_stack(src_stack,dest_stack,num_counter):

     # Move num_counters counters from stack src_stack to stack dest_stack



     global stacks,move_count



     num_counter=int(num_counter)

     if num_counter<1:

         print("Counters to move must be >= 1")

    

    

     if (src_stack=="a" and dest_stack=="b") or (src_stack=="b" and dest_stack=="a"):

         inter_stack="c"

     elif (src_stack=="a" and dest_stack=="c") or (src_stack=="c" and dest_stack=="a"):

         inter_stack="b"

     elif (src_stack=="b" and dest_stack=="c") or (src_stack=="c" and dest_stack=="b"):

         inter_stack="a"

     else:

         print("Error, source and destination must be in 'a', 'b', 'c'")

         return false

    

     if num_counter==1:

         # move 1 counter, then we're done

         counter=stacks[src_stack].pop()

         stacks[dest_stack].append(counter)

         move_count+=1

         #         print(f"Moved counter {counter} from {src_stack} to {dest_stack}, moves={move_count},  {stacks}")

     else:

         # Move n-1 counters to intermediate stack, move 1 counter to destination, move n-1 counters from intermediate stack to destination

         move_stack(src_stack,inter_stack,num_counter-1)

         move_stack(src_stack,dest_stack,1)

         move_stack(inter_stack,dest_stack,num_counter-1)



def do_hanoi(num_counters):

     # Setup and run the problem, num_counters is number of counters to load on first stack

    

     global stacks

     global move_count

    

     move_count=0

     stacks={"a":[],'b':[],'c':[]}

     # Load the initial stack

     for i in range(num_counters,0,-1):

         stacks['a'].append(i)

    

     move_stack('a','c',num_counters)

    

     print(f"Towers moved in {move_count} moves")

    

do_hanoi(3)

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