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My friend dislikes Rubik's cubes, and he asked me how to frustrate amateur solvers by adversarially scrambling the cube. I expect that the answer depends highly on the particular solving algorithm.

Are there "human" algorithms for solving a Rubik's cube that are known to be very inefficient (compared to optimal) against particular "bad" configurations?

By "human", I mean the common algorithms that are taught in practice to amateurs or used by enthusiasts. There might be too much variety in common human techniques for this question to make sense, but even that would be good to know. (I'm looking for something more interesting than naive random walk, which is clearly almost always inefficient.)

And the relevant followup question:

Are there ways to find these bad configurations by applying random moves?

That is, is there an easy way to randomly generate hard cube instances for a particular human algorithm?

This is (somewhat) related to another question of mine about shortest paths to solution when randomly scrambling a Rubik's cube.

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  • $\begingroup$ It would also be interesting to compare the minimum distance of a starting position and the time needed by an expert to solve it from an official World Cube Association competition. $\endgroup$ – Marzio De Biasi May 9 '12 at 10:20
  • $\begingroup$ With the algorithm I learnt, I don't think that any position is especially worse than any other, and besides that, when I used to use it, I would actually prefer a position that required me to go through all the steps of my algorithm, so the only way to frustrate me would have been to make it too easy! $\endgroup$ – Tara B May 11 '12 at 12:57
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If the aim is to frustrate amateur solvers, maybe the best is to give them a configuration that seems very simple to solve, but will be hard with the common algorithms. For instance you can just invert all the centers, or do a few swaps between squares, to have just 1 or 2 wrong on each face. This is of course betting they don't know the special algorithms to create/solve these special configurations ;)

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    $\begingroup$ Keep in mind that a common technique used by amateur solvers (including me) is the "screwdriver technique", which is very efficient against every hard configuration :-) (just kidding) $\endgroup$ – Marzio De Biasi May 9 '12 at 22:09

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