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?



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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