Solution #1 (Step 5)

Step 5 -- Position U face corner pieces

Now we must move the corner pieces into the right places.
There are 3 possibilities:

• All 4 corner pieces are in the right place, although not necessarily rotated correctly. Do nothing.
• 1 corner piece is in the right place. Hold the cube so that it is in the UFR position. If the remaining three corner pieces need to be rotated clockwise, apply L' U R U' L U R' U'. If they need to be rotated counter-clockwise, apply U R U' L' U R' U' L.
• 0 corner pieces are in the right place. If they all need to go to opposite corners, apply R' B2 F R F' R' F R F' R' F R F' R' B2 R. If they need to go to adjacent corners, hold the cube so that UFR and UFL pieces need swapping, and so do the UBR and UBL pieces. Apply B L U L' U' L U L' U' L U L' U' B'.

Okay, now all of the corner pieces should be in the right place. We're almost there!