Towers of Hanoi Recursive Explanation in Ruby

Towers of Hanoi Recursive Explanation in Ruby

I'm having a difficult time understanding the recursive loop for the
Towers of Hanoi. I've commented and tried various tactics to see how the
procedure is operating, but I can't seem to grasp how the loops are
operating and how the rings are being directed.
def move(rings, from, destination, other)
if rings == 1
ring = from.pop
p "Move ring #{ring} from #{from} to #{destination}"
destination.push ring
else
move(rings-1, from, other, destination)
move(1, from, destination, other)
move(rings-1, other, destination, from)
end
end
Here's the output:
"Move ring 1 from a to c"
"Move ring 2 from a to b"
"Move ring 1 from c to b"
"Move ring 3 from a to c"
"Move ring 1 from b to a"
"Move ring 2 from b to c"
"Move ring 1 from a to c"
I've looked at various cases on this, but I don't see an explanation for
how the loops are being executed. For instance, I can't figure out why is
is it the case that when the rings are even, the first step places ring 1
from a to b, while for all odd number of rings, it's from a to c, as shown
above.
I understand the logic behind the solution, that in order to move n number
of rings to a destination while using an auxiliary peg requires that you
first move n-1 number of rings to the auxiliary peg followed by moving the
nth ring to the destination and repeating the same procedure. But, I'm
unsure how the directions for placement are changing, furthermore, I don't
see how a block is going from c to b when the call to the move method,
above, doesn't seem to mention c to b.
Thank you, in advance, for your time and help.
Also, if you have any suggestions for helping track the process of code
executions in Ruby, please let me know. I'd love to hear some of your
insights to how you'd troubleshoot instances where you're unsure how
things are being executed.
Eager to hear your answer :)