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Because each state requires 0 or 1 hits in order to achieve the correct state (the sword thing, in this case), the shapes themselves can be abstracted away and you basically have a "Travelling Salesman" situation, do you not?
If so, your problem is NP-Complete, and intractable. If you solve it, you'd be eligible for almost $7 million in research rewards for solving NP-Complete problems of this type.
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