I feel like practically anybody could solve Tower of Hanoi for any degree of complexity using this algorithm. It’s a four step process that you just repeat over and over.
That's an algorithm to solve it, but you have to describe every move at every step, while doing this on paper or in your head, while keeping track of the state of the game, again, in your head. That is what they're challenging the LLM to do.
You're still misunderstanding. If it is easy, please feel free to demonstrate solving it by telling us what the 1300th step is from working it out in your head.