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There's a very good book by Hinz, Klávžar, Milutinović and Petr, called "Towers of Hanoi - Myths and Maths".
It collects all sorts of theorems and perspectives on the puzzle, and plenty of variants.
Published by Springer:

One variant that's easy to describe but hard to play is Twin Towers: get two sets, and each move consists of nominating two towers and making the valid move between them on both sets simultaneously.
Investigated by Zoran Šunić: read.somethingorotherwhatever.