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Instructions
Solve the bottom layer of the cube first by matching the colors up in pairs along the lower half. You should be able to line them up with a few twists of the cube.
The color that does not appear in the bottom row will be the top face of the cube. Rotate the top to get one of the corners in place with that missing color. The color need not be on the top of the cube itself, but can be on the side of one of the cubes in that position.
Swap adjacent corners of the top side of the cube by following this sequence while keeping the cube in the same position relative to you. Turn the top side counter-clockwise once, the back side counter-clockwise once and the top side counter-clockwise once. You will then turn the back side clockwise once, the top side clockwise once, the left side clockwise once and the top side counter-clockwise once.
Swap colors that are next to each other on the top side of the cube with this sequence: Turn the front side clockwise once, the top side clockwise once, the front side counter-clockwise once, the top side counter-clockwise once, the left side counter-clockwise once, the top side counter-clockwise once and then the left side clockwise once.
Do the two maneuvers in Steps 3 and 4 as needed to switch colors next to each other or adjacent to each other until the top side colors are all in position on the top half of the cube. The correct color may not be on top--for example, your top section might not be all white or all green yet--but you should have each of the color you need in position at the top. For instance, if you need white on top, you may have a white square on top and another on the upper right face. As long as they are all in the upper plane, you can proceed to the next move.
Rotate the individual pieces at the top of the cube to get them all one color. To rotate a corner piece clockwise, turn the right side clockwise once, the down side clockwise twice, the right side clockwise once, the front side clockwise once, the down side clockwise twice and the front side counter-clockwise once.
Rotate another corner counter-clockwise after turning the initial piece clockwise. Turn the top side until the corner you need to move is in the upper-right of the front side as you face it. Then turn the corner counter-clockwise by turning the front side clockwise once, the down side clockwise twice, the front side counter-clockwise once, the right side counter-clockwise once, the down side clockwise twice and the right side clockwise once.
Alternate the two moves in Steps 6 and 7 to get the top corners positioned correctly and the cube is solved.