>>thomas+(OP)
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*).
>>thomas+(OP)
The problems themselves aren’t particularly interesting, I suppose. The interesting part is how the complexity of each problem scales as a function of the number of inputs (e.g. the number of disks in the tower of Hanoi).