Hanoi Stack comes from Sergii Nagin. Th object is to flip rings and stacks of rings to eventually land on the pole is size order - largest on the bottom.
1. Multiple rings of the same size are frequent.
2. When a stack joins another ring, it will invert completely. Look at the last image. The green ring on top - that whole stack will flip onto the light blue ring. That will leave the red, largest ring, on top.
I have no idea how many levels there are. I've done about 120. The last 25 took about 20 minutes.