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Curvy Copter shape: Is it possible to jumble a single corner and center like so?

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Dec 28, 2009
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I can definitely solve a jumbled curvy copter as long as it's in a cubic shape. I had formerly believed I could solve any jumbling, until I let someone else scramble it. They managed to jumble it in such a way that there was an odd number of flipped corner-center pairs. It looked like they were really forcing the pieces, so I suspect they've made an "illegal" move.

I can flip two pairs at a time, but that means I get stuck with a single pair, as in the attached photo. Is this a commonly reachable jumbling, or should I reassemble the puzzle?

IMG_20190331_143001.jpg

Note: When I say "flip" I'm talking about fixing the whole cube orientation, not permuting just those two pieces.
 
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