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The bottom two layers are solved, and the cross has been formed on the bottom layer. I am putting the corners in, ready to orientate them correctly, but I have two corners which need swapping. (The 719 and 341 corners on front and back left so it has the right orientation to the centre piece being the correct way)

I didn't think this was possible, but I have borrowed this from someone and they have assured me no pieces have been swapped!

I've tried to add different views to help show the rest is solved.

enter image description here enter image description here

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  • $\begingroup$ I would describe how to do it, but I'm not home nor do I have immediate access to my cubes $\endgroup$ – dcfyj Jan 30 at 19:26
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It is possible to swap two corners, but doing so will also swap two edge pieces. It is possible that there are two edge pieces on the cube that are identical, and swapping those two will not be visible, so that you can in effect swap two corners without seeming to have any effect on the edge pieces.

Notice that the centre square showing a 5 is twisted by a quarter turn. If you solve the corners relative to that 5, you'll find that you don't need to swap 2 corners, but that actually only one is in its correct place and you need to cycle the other three corners around. This also means that the four edges around that 5 are essentially all in the wrong location. You can put two of the edges correct by cycling 3 of them around. That leaves two edges that need to be swapped, which can only be done by also swapping two identical edges elsewhere in the cube.

To do this a bit more directly, you could use the following PLL move sequence (a J-perm): RU2R'U'RU2 L'UR'U'L
This swaps the two corners in the right hand side (UFR, UBR), swaps two edges (UF, UR) and twists the centre to the left.

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