Placing the corners

The top is solid yellow, but the corners are probably standing in the wrong places. This step moves them into the right ones without disturbing which way up they are.

A corner is home when its two side colours match the two centres it sits between — a red-and-green corner in the gap between the red face and the green face. It does not matter that the sides look jumbled elsewhere; check that one corner on its own.

Finding the one that is already right

Turn the top face and look after each quarter turn. There is always a position in which at least one corner is home — the cube cannot deny you one. Stop there.

The algorithm

Hold the cube with the corner you found at the front-left, on the top layer. Running the algorithm sends the other three round clockwise, seen from above: front-right goes to back-left, back-left goes to back-right, back-right comes to front-right.

So look at where your three loose corners need to travel. If that journey is clockwise, one go does it. If it is anticlockwise, run it twice — the second go carries them the rest of the way round.

1. Turn the top face until at least one corner is home.
   U
2. Turn the whole cube so that corner is at the front-left. Do not turn the top again.
   y
3. Work out whether the other three need to go clockwise or anticlockwise.
4. Clockwise: run it once.
   R^'FR^'B²RF^'R^'B²R²
5. Anticlockwise: run it twice, without changing your grip in between.
   R^'FR^'B²RF^'R^'B²R²

When you can never find exactly one

Occasionally you will turn the top all the way round and never see a single home corner on its own. Instead you find two positions where two corners are home, sitting diagonally opposite each other, and two where none is.

That position cannot be finished by a three-corner rotation, because the two corners that are wrong need to swap rather than travel. The fix is to stop trying to be clever: hold the cube any way round and run the algorithm once. It breaks the diagonal up, one corner lands home, and you carry on exactly as above.

What finished looks like

The top is yellow and all four corners are home: every corner of the cube has its three colours matching the three faces it touches. Only four edges are still adrift, and there is one step left.