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I saw videos of people participating in race to resolve a Rubik cube as quickly as possible using Mindstorm LEGO robots.

Can you provide information if there is a competition, who is involved? What is the research/design process? Is there any sponsorship? What are the performance obtained?

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There's no "race" as this has been solved multiple times by different people (solving rubik's cube isn't that hard). just take a look at the CubeStormer (or, better, the CubeStormer II).

I also saw building-plans and programs for such a cube-solver (not exactly the linked one). If you like to rebuild such a thing: I'll add links as soon as i find them.

EDIT:
As promised, there's the Tilted Twister with building plans online. See it in action on this youtube-video. This is very slow compared to the CubeStormer, but looks like it can be built using only the NXT2.0-pack and doesn't need thousands of parts and multiple expensive NXT-logic-blocks.

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    I beg to differ :) The race to lower the cube solving time is still on. gizmodo.com/5850505/… The plans for the tilted twister in your answer are awesome! – jfyelle Oct 27 '11 at 13:45
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    The Tilted Twister is great! – Coyote Oct 27 '11 at 13:45

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