Rubik's Cube Nuggets

Solving the cube using computer-generated sequences of moves - by Don Cross

This web page contains useful tricks for solving Rubik's Cube that were found by a computer program I wrote in June 2002. The computer program simulates a Rubik's Cube and tries millions of different combinations of moves, until it finds combinations that affect the corners and edges on only one of the 6 planes of the cube. The original document was a Microsoft Excel spreadsheet. I optically scanned the diagrams from an old printout of that spreadsheet, hence the somewhat degraded image quality.


Glossary

Note that many of the words are defined in terms of each other. When a defined word appears in the definition of another word, the defined word is italicized.

word definition
corner One of the 8 pieces of the Rubik's Cube that has 3 tiles on it.
cost The number of face rotations needed to perform a nugget.
cycle To move 3 edges/corners from position A to position B, B to C, and C to A.
edge One of the 12 pieces of the Rubik's Cube that has 2 tiles on it.
flip To rotate the orientation of an edge (there are 2 possible orientations).
mirror The mirror image of a nugget, with the mirror held parallel to the cube's right face.
nugget A sequence of moves on the Rubik's Cube that performs a desired operation.
reverse The inverse of a nugget, meaning the sequence of moves that would undo the nugget.
spin To rotate the orientation of a corner (there are 3 possible orientations).
swap To move 2 edges/corners from position A to B and B to A.
tile One of the colored faces of either an edge or a corner.


Move Notation

f front
p posterior
r right
l left
t top
b bottom
x right and left (x+ = r+l-)
y front and posterior (y- = f-p+)
z top and bottom (z+ = t+b-)
+ clockwise (looking into the moved face)
- anticlockwise (looking into the moved face)
2 180-degree turn

N1: Cycles 3 corners on the top face, spinning one clockwise and one anticlockwise.

            f+
            r+
            f-
            l+
            f+
            r-
            f-
            l-
            
diagram of N1

N2: Cycles 3 edges without flipping any of them.

            f2
            t+
            x-
            f2
            x+
            t+
            f2
            
diagram of N2

N3: Cycles 3 edges, flipping 2.

            x-
            f+
            x+
            t2
            x-
            f+
            x+
            
diagram of N3

N4: Swaps 2 corners and 2 edges, with no flipping/spinning.

            f2
            r+
            t+
            r-
            f2
            l+
            b-
            l+
            b+
            l2
            
diagram of N4

N5: Spins 3 corner cubes anticlockwise and cycles 3 edge cubes.

            r-
            t-
            r+
            t-
            r-
            t2
            r+
            t2
            
diagram of N5

N6: Cycles 3 edges, flipping 2 of them.

            f-
            t-
            f+
            x-
            b-
            f+
            b+
            x+
            
diagram of N6

N7: Swaps 2 pairs of opposite edges, flipping one in each pair.

            f-
            t-
            l-
            t2
            l+
            f+
            t+
            r+
            t2
            r-
            
diagram of N7

N8: Spins 3 corners anticlockwise, and flips 2 edges.

            r+
            t+
            r2
            f+
            r+
            f2
            t+
            f+
            t2
            
diagram of N8

N9: Cycles 3 corners, spinning each clockwise.

            f+
            r-
            t2
            r+
            f-
            r-
            f+
            t2
            f-
            r+
            
diagram of N9

N10: Swaps both diagonally opposite corners, with no spinning of any.

            f2
            x2
            p2
            b-
            f2
            x2
            p2
            t-
            
diagram of N10

N11: Flips 2 adjacent edges.

            t+
            f+
            t+
            f2
            b-
            l-
            t-
            l+
            t+
            b+
            f2
            t2
            f-
            
diagram of N11

N12: Flips 2 opposite edges.

            t+
            y+
            r-
            t+
            f-
            r+
            t-
            y-
            l+
            t-
            f+
            l-
            
diagram of N12

N13: Spins 2 opposite corners.

            t2
            r+
            f-
            b2
            f+
            r-
            t2
            r+
            f-
            b2
            f+
            r-
            
diagram of N13

N14: Flips all 4 edges on top face.

            t+
            x+
            f2
            r2
            b2
            r2
            p+
            r2
            b2
            r2
            f2
            x-
            
diagram of N13