Towers of Hanoi IS an algorithmic problem. It is a high-school/college level problem when designing algorithms, probably kid level when trying to solve intuitively, heuristically or via brute force for few disks (i.e. like when playing Mass Effect 1 or similar games that embed it as a minigame*).
* https://www.youtube.com/watch?v=1vTBVyhX7n4