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What is the minimum number of turns needed to solve a rubik's cube with one edge piece faced the wrong way on the 3rd layer?

Example

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4
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Not possible.
For one cubelet to be off like that indicates that the cube was misassembled. See here - any legal rotation or combination of rotations that involves flipped edge cubes will result in an even number of flipped edge cubes.

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  • $\begingroup$ There is also puzzling.stackexchange.com/questions/521/… that asks essentially the same question, and the same principle applies to puzzling.stackexchange.com/questions/20/…, which should be considered an answer to both this question and the edge question I linked to. $\endgroup$ – Jeff Zeitlin Jan 3 '17 at 17:40
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    $\begingroup$ @BeastlyGerbil - why spoilerize this? The situation is impossible, and not making that clear immediately does not seem reasonable. $\endgroup$ – Jeff Zeitlin Jan 3 '17 at 17:42
  • $\begingroup$ I was going along the lines that someone who sees this might want to try this on their own, and that some people might want to see the answer $\endgroup$ – Beastly Gerbil Jan 3 '17 at 17:47
  • $\begingroup$ "Ah yes let me just try flipping an edge piece on my own for two hours..." $\endgroup$ – greenturtle3141 Jan 3 '17 at 21:11
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    $\begingroup$ @greenturtle3141 I've met some weird people when it comes to rubiks cubes... $\endgroup$ – Beastly Gerbil Jan 4 '17 at 7:20

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