Essential Rubik's Cube Algorithms: The 5-Formula Beginner's Cheat Sheet

All Beginner Algorithms on One Table

Because our beginner's method keeps the white face on top (U) and solves the last layer on the bottom (D), you never flip the cube upside down. Learn each formula in four-move chunks—every four-move chunk feels like drawing a small square with your hands:

The Bottom Four-Move Algorithm: R' D' R D and Its Reverse D' R' D R

In Stage 2 (White Corners), your goal is to lift a white corner from the bottom front-right position (DFR) into the top front-right slot (URF) without disturbing the white cross you already built. The bottom four-move algorithm accomplishes this by swapping those two corners back and forth while rotating their stickers:

Depending on which way the corner's white sticker is pointing before you start, repeating R' D' R D inserts the corner in 1, 3, or 5 repetitions:

• White sticker faces right: 1 repetition of R' D' R D solves the corner immediately.
• White sticker faces down (toward the floor): 3 repetitions of R' D' R D in a row solve the corner.
• White sticker faces you (front): 5 repetitions of R' D' R D solve it—or use a single reverse bottom trigger D' R' D R to insert it in just 4 moves!

The Top Four-Move Algorithm (“Sexy Move”): R U R' U'

In the speedcubing community, R U R' U' is famously called the sexy move because it flows effortlessly off the index fingers and wrists. In our beginner's method, it is used in Stage 7 to twist each bottom-layer corner until its yellow sticker faces down:

Do not mix up the two triggers! In Stages 2–4, you want to protect the top white layer, so you use the bottom trigger (R' D' R D). In Stage 7, you want to protect the bottom yellow edges while twisting one bottom-front-right corner, so you use the top trigger (R U R' U') 2 or 4 times per corner.

Middle-Layer Edge Insertion (Right and Left)

In Stage 3 (Second Layer), the top white face is already complete, and you need to move an edge from the bottom layer into the middle-right or middle-left slot without breaking any solved white pieces. Notice how the right insertion is simply two four-move triggers back to back:

How it works mechanically: the first four moves (D' R' D R) temporarily pull the solved front-right white corner out of the top layer and pair it up with the middle-layer edge. The second four moves (D F D' F') re-insert both pieces together from the front side. The left insertion is the exact mirror image with the left hand:

The Yellow Cross Conjugate: F' (R' D' R D) F

In Stage 4 (Yellow Cross), you flip yellow edges on the bottom face without disturbing the first two layers. Look closely at the structure of the 6-move formula:

In group theory, a sequence of the form A · B · A' is called a conjugate (or “setup move + trigger + undo setup”). You turn the front face counterclockwise (F'), run a single bottom four-move trigger (R' D' R D), and turn the front face back clockwise (F). Each application advances the bottom yellow edges by one step along the chain: Dot → L-shape (held back-left) → Horizontal Line → Yellow Cross.

The Fish (Bottom Sune): R D R' D R D2 R'

Once the yellow cross is formed on the bottom face, Stage 5 aligns the four bottom edges with their side centers. This 7-move algorithm (known as Sune when executed on the top layer) cycles three bottom edges while keeping the yellow cross intact:

How to track it visually: the first move (R) lifts the solved white-red-blue corner pair out of the first two layers into the bottom layer; D R' D pushes that pair toward the back while restoring the right column; and R D2 R' sweeps the pair all the way around to reunite with the top layers.

The Corner 3-Cycle (Niklas): D' R' D L D' R D L'

In Stage 6, all four yellow edges are in place, and you need to move the four bottom corners to their correct home slots without scrambling the edges. This 8-move commutator (known as Niklas) keeps the front-right-bottom corner (DFR) in its slot while cycling the other three bottom corners around:

Notice the rhythmic symmetry: the bottom face always alternates D' then D. In the first half, both side layers move toward the floor (right down R', left down L). In the second half, both side layers return upward (right up R, left up L').

Why Repeating R U R' U' Six Times Restores the Cube

Both R U R' U' and R' D' R D are mathematical commutators of the form [A, B] = A · B · A' · B'. Because the two layers only intersect along a single 3-piece strip (two corners and one edge), almost every piece moved by A and B is immediately put back by A' and B'.

• A single execution of R U R' U' swaps two pairs of corners (a 2-cycle on top and a 2-cycle along the right column) and cycles 3 edges (a 3-cycle).
• After 2 repetitions ((R U R' U') × 2), the corner swaps cancel out completely (2 divides 2), leaving the corners in their original positions (with two corners twisted) while the 3 edges continue cycling.
• After 3 repetitions ((R U R' U') × 3), the 3-cycle of edges returns to its starting position (3 divides 3), leaving only two pairs of swapped corners!
• After 6 repetitions (lcm(2, 3) = 6), both the 2-cycle of corners and the 3-cycle of edges complete full cycles, and every corner twist sums to a multiple of 3—returning a solved cube back to its exact starting state.

Practice these algorithms step by step in Train mode