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We are trying to solve variant of the n-peg Tower of Hanoi problem. There can be limitations on possible moves among the pegs. In the graph vertices are pegs, and an edge from vertex to another tells us we can move a disk from the first peg to the other.

We need to find out what are the necessary and sufficient conditions the graph must have so that the problem of Hanoi can be solved, and if there is an algorithm for solving it.

Help will be much appreciated.

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  • $\begingroup$ Probably the answer will depend on the starting configuration as well. Is the starting configuration given? Are we limited so that no disk is ever allowed to be placed on top of a smaller disk (as in the usual Tower of Hanoi problem)? Are you looking for an efficient algorithm, or any algorithm at all (regardless of how inefficient it may be)? $\endgroup$ – D.W. Aug 6 '17 at 18:10
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    $\begingroup$ Can you specify the problem more formally? A lot is left unstated in your question. What are the rules? What is the goal? $\endgroup$ – Yuval Filmus Aug 6 '17 at 20:54
  • $\begingroup$ Please edit the question to clarify the problem statement, per comments above. When the question is edited, it can be considered for re-opening. Thank you. (And welcome to the site, by the way!) $\endgroup$ – D.W. Aug 7 '17 at 19:28