How to Scramble a Rubik's Cube the WCA Way

What is a scramble?

A scramble is a list of moves written in notation, for example:

D2 F' R2 U' L2 B2 U F2 D' R2 B L' U2 F' R D' B2 R' U L

You start from a solved cube and do exactly those moves. Everyone who does them correctly ends up with the same scrambled cube. That way, two people in two different places can solve the same case and compare times fairly.

In the picture below, a solved cube should look like the left side after you do the scramble above. The right side shows that doing the sequence backwards brings the cube back to how it was (how to do it backwards comes later).

1. You start with (input)
3. After the formula

According to the Speedsolving Wiki, an official 3x3 scramble is usually about 20 moves long.

Reading the notation in a scramble

A scramble uses the same notation as algorithms. The WCA Regulations (article 12a) give six letters for the six faces:

• A letter on its own (R): turn that face 90 degrees clockwise, as you look straight at that face.
• With an apostrophe (R'): turn it 90 degrees anticlockwise.
• With a 2 (R2): turn it half a turn (180 degrees). Either direction works, the result is the same.

For example, the move R turns the right face. The picture below shows one R move turning the cube on the left into the cube on the right:

1. You start with (input)
3. After the formula

The back (B) and bottom (D) faces are the easiest to turn the wrong way, because you are not looking straight at them. Tip: imagine walking round to the back of the cube, or crawling underneath it, then turn clockwise from there. If these letters are new to you, see Rubik's Cube notation for beginners first.

Hold the cube the right way: white on top, green in front

Article 4d1 of the WCA Regulations says an NxNxN cube is scrambled with the white face on top and the green face in front. On a cube with the standard colour scheme, holding it like that puts red on the right, orange on the left, blue at the back and yellow on the bottom.

If your cube has no white, the rules say to use the lightest colour on top. If it has no green, use the darkest colour next to the top face in front. The rules also make it clear: on a cube where black replaces white, black counts as the darkest colour and must not be treated as white.

You only need to look at the centres of the top and front faces. Centres never move when you turn a face, so on a solved or unsolved cube, the centres still tell you how to hold it.

How to scramble a Rubik's Cube, step by step

1. Solve the cube first. A scramble only works if you start from a solved cube.
2. Hold it white on top, green in front. From here to the end of the scramble, do not rotate the whole cube in your hands.
3. Do one move at a time, in order. Read slowly, one move at a time. You can read them out loud, or point at the move you are on with your finger.
4. Count again. A 3x3 scramble has about 20 moves. If you finish and there are still letters you have not read, you skipped one somewhere.
5. Check against the picture. If the program shows a picture of the scrambled cube, put your cube next to it and compare the top, front and right faces.

Try it with the scramble at the top of this post. The correct result is the left side of the picture below:

1. You start with (input)
3. After the formula

It is the same at competitions: article 4g says the scrambler must check the cube again after scrambling. If the cube is wrong, they have to fix it, for example by solving it and scrambling it again.

What if you scramble it wrong?

If you know which move went wrong, you can undo your way back. The rule for undoing a sequence of moves:

• Go from the last move back to the first.
• Flip the direction of each move: R becomes R', R' becomes R. Moves with a 2 stay the same.

For example, the reverse of R U F' is F U' R'.

1. You start with (input)
3. After the formula

Reverse the whole scramble from the top of the post and you get:

L' U' R B2 D R' F U2 L B' R2 D F2 U' B2 L2 U R2 F D2

Do this on a correctly scrambled cube and it goes back to solved, like the first picture in the post. If you do not know where it went wrong, the surest fix is to solve the cube and scramble it again from the start, just like the WCA rules do.

Common scrambling mistakes

Holding the cube the wrong way

This is the most common mistake. Same scramble as above, but if you hold the cube with yellow on top (green still in front), you get a completely different cube. The picture below shows the cube held in exactly that wrong way:

1. You start with (input)
3. After the formula

Compared with the correct picture above, the faces do not match, even if you flip the cube over so white is on top. Beginners often hold yellow on top because the layer-by-layer method solves the white face on the bottom. Remember: scramble with white on top, solve however you like.

One wrong move

Just one wrong move changes the whole cube. For example, if on the fourth move you do U instead of U', with every other move right, you get the cube on the left below instead of the correct one:

1. You start with (input)
3. After the formula

Moves that are easy to mix up: R' with R, and B and D (the faces you cannot see). Read slowly on those moves.

Rotating the whole cube halfway through

When turning B or L, a lot of people tilt the whole cube to see better and forget to turn it back. From then on, every move after that turns the wrong face. Keep the cube still and bring your fingers to the face you need to turn.

Skipping or repeating a move

This tends to happen when the scramble has several similar moves close together, like R2 ... R2. Count the moves, or cover the part you have done with your finger.

Why does the WCA scramble with a computer?

Under article 4b, competition scrambles must be made with the current version of the official WCA scramble program. That program is TNoodle, made by the WCA, with its source code published on GitHub. According to the project page, only the scramble-generating part is official, and competitions may not use a modified version.

The rules add a few more things to keep it fair:

• No picking (4b1). Organisers may not look at, filter or regenerate the scramble sets to get "easier" or "fairer" ones.
• Kept secret (4b2). Before a group starts, only the WCA Delegate may see the scrambles. Organisers should screen off the scrambling area, so competitors cannot see the scramblers or the cubes being scrambled.
• Same group, same scrambles (1h). Competitors in the same group solve the same scrambles, so nobody gets an easier cube than anyone else. You can read more about how a round works in WCA Rubik's Cube competitions.

Random-state: every state has the same chance

There are two ways to make a scramble:

• Random-move: pick about 20 to 25 moves at random. Easy to do, but some states come up more often than others.
• Random-state: the computer picks one state at random out of every possible state of the cube, then finds a sequence of moves that leads to it.

The Speedsolving Wiki explains that the second way gives a fully random state, with no bias towards easy solutions. The wiki also says that 25-move random-move scrambles, still often used for practice, are "slightly less random" than official ones.

WCA article 4b3 says an official scramble must give a random state out of the states that need at least 2 moves to solve. In other words, at a competition you will never get a cube that is solved in just 1 move.

Scrambling other cubes

The way you hold it (white on top, green in front) is the same for every NxNxN cube. What changes is how the scramble looks.

Rubik's 2x2

According to the Speedsolving Wiki, official 2x2 scrambles only use three faces: R, U and F. Article 4b3 also says the 2x2 state must need at least 4 moves to solve. A scramble looks like this:

U2 F R' U F2 R U' F' R2

1. You start with (input)
3. After the formula

The left picture is the 2x2 after doing the scramble above from a solved cube.

Rubik's 4x4 and bigger

Bigger cubes add moves that turn the two outer layers together, written with a w (article 12a2). For example, Rw turns the right face together with the layer next to it. Part of a 4x4 scramble, as an example:

R Uw2 F' Rw U2 Fw

1. You start with (input)
3. After the formula

Under article 4b3, the 4x4 also uses random-state scrambles. The 5x5, 6x6 and 7x7 use random-move scrambles instead. The Speedsolving Wiki gives the lengths as 60 moves for 5x5, 80 for 6x6 and 100 for 7x7.

Scrambling when you practise on your own

At home, you do not need TNoodle. A few tips:

• Do not just twist the cube randomly by hand. Random twisting often leaves lots of pieces close to where they belong, and you cannot solve that same case again to compare. Use a scramble from a program.
• Use the EasyRubic [3x3 timer](/vi/timer/3x3). Every solve, the timer gives you a new scramble plus a picture of the scrambled cube to check against. Its 3x3 scrambles are 20 moves long and made by random moves, never turning the same face twice in a row. That is good enough for practice, though not exactly the same as competition random-state scrambles.
• Get scrambling right from the start. At a competition, you do not scramble your own cube. But if you later help the organisers as a scrambler, scrambling quickly and correctly is a skill you will need.

Sources

• WCA Regulations (Article 4: Scrambling; Article 12: Notation)
• TNoodle – official WCA scramble program, World Cube Association (GitHub)
• Scrambling – Speedsolving.com Wiki
• Random State Scramble – Speedsolving.com Wiki