Tower of Hanoi

When playing the tower of Hanoi puzzle, I noticed that to finish, one had to utilize all three pillars. I did not really find any specific rhythms or strategies for finding the fasted solution, but I did notice that one had to go against their instinct to complete it. Mathematical induction is seen in this puzzle through the reoccurring steps that include using all three towers. This proves that to get all the rings on the last tower, the middle tower must always be used. This is an inevitable  pattern that occurs whether there are 2 rings or 6.