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You'd have to do that for VxVxV, because there are three different objects (although there's some symmetry). Solving a puzzle is often described as path finding.


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The vast majority of states is not reachable, so you can roll out the full tree from the starting state and it's going to be very small. Even the super-naive approach of unrolling the full state space is only 6^7 which is a big waste because connections are very sparse but even that's not big, it just wouldn't scale to larger problems.

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