Sierpiński triangle
Towers of Hanoi

The Towers of Hanoi puzzle involves moving disks of different sizes between three pegs, maintaining the property that no disk is ever placed on top of a smaller disk. The states of an n -disk puzzle, and the allowable moves from one state to another, form an undirected graph, the Hanoi graph, that can be represented geometrically as the intersection graph of the set of triangles remaining after the n th step in the construction of the Sierpinski triangle. Thus, in the limit as n goes to infinity, this sequence of graphs can be interpreted as a discrete analogue of the Sierpinski triangle.
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