I'm trying to fully understand how the recursive Towers of Hanoi Algorithm works and to implement it in code.
Something that keeps throwing me of is the use of phrases like "move n-1 discs from A to B using C."
I understand that the peg which is referred to is as being "used" is the auxiliary or spare peg, but the language seems misleading because if n-1 has a value of more than 1, then more than one peg is used to perform the move. So the phrase "using C" or "using B" or "using A" doesn't seem accurate and is hindering me from thinking clearly about the problem.
Am I missing something, or can I substitute the phrase "with C as the spare/auxiliary peg" for "using C" without loss of meaning?
I've seen one video where for the n=2 problem, the first move is described as "move a disc from A to B using C" - in this case C isn't involved at all!
I wonder if anyone who has managed to fully grasp the algorithm can advise if it would be helpful to adopt the "using A/B/C" language or if there is another alternative that you have found more helpful, such as my suggestion above - "with C as the spare/auxiliary peg"?