# Solving the Tower of Hanoi by using a good state space and then a search tree

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I want to solve the "Towers of Hanoi" problem by using a good "state space". Using an appropriate state space is a way that is suggested by some AI techniques. Having a good state space, I would then like to be able to build a search tree and then use some strategy like "DFS" (depth-first-search) to find a solution.

My problem is, I just don't know how to develop a good state space and then use it to build a search tree. Can anyone describe how to create a state-space for the Tower of Hanoi problem? Then tell me how to build a search tree for that?

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In this article, there is a concept of a state-space and the different searches that can be used to explore the search space to find a solution. Before an AI problem can be answered it must be represented as a state space. The state space is then searched to find a solution to the problem. A state-space consists of a set of nodes representing each state of the problem, arcs between nodes representing the legal moves from one state to another, an initial state and a goal state. Each state area takes the form of a tree or a graph.

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