Confident · ages 13+ · lists · permutations · while loop · maths

Simulate a 2×2 Rubik's Cube move in Python.

Represent a 2×2 cube as 24 stickers, apply the moves R and U as rearrangements, and count how many times R U repeats before the cube is solved again.

The program

Press Run to see what it prints. Change anything you like, then run it again.

# Stickers are numbered 0 to 23 (6 faces of 4). A move says where each sticker goes.
R = [0, 22, 2, 20, 5, 7, 4, 6, 8, 1, 10, 3, 12, 9, 14, 11, 16, 17, 18, 19, 15, 21, 13, 23]
U = [1, 3, 0, 2, 8, 9, 6, 7, 16, 17, 10, 11, 12, 13, 14, 15, 20, 21, 18, 19, 4, 5, 22, 23]

def apply(state, move):
    new = list(state)
    for i in range(24):
        new[move[i]] = state[i]
    return new

solved = list(range(24))
state = solved
repeats = 0
while True:
    state = apply(apply(state, R), U)
    repeats = repeats + 1
    if state == solved:
        break
print("R U repeats", repeats, "times on a 2x2 before the cube is solved again")

R U repeats 15 times on a 2x2 before the cube is solved again

How it works

The cube has 24 stickers. A move is a list that says which place each sticker goes to. Doing a move means moving every sticker to its new place.
apply makes a new list and puts each sticker where the move sends it. Doing R and then U is two calls to apply.
The loop repeats R U until every sticker is back where it began. The count is the order of the move. See the maths of the cube for the 3×3 version.

See the Python path →

Try this

Count the repeats of R alone. What do you expect?
Try three moves in a row, such as R, U and R again.
Print the state after one R U to see the rearrangement.

Stuck on an error? Read how to debug Python.

Similar ideas

More programs

All programs →

Countdown

Count down from 10 and finish with a message.

Beginner · ages 8+

Fibonacci numbers

Build the Fibonacci sequence, where each number is the sum of the two before it.

Easy · ages 10+

The Collatz sequence

Start with any number. If it is even, halve it; if odd, triple it and add 1. See how long it takes to reach 1.

Easy · ages 11+

FAQ

Simulate a 2×2 Rubik's Cube move: questions

What does the simulate a 2×2 rubik's cube move program do?

Represent a 2×2 cube as 24 stickers, apply the moves R and U as rearrangements, and count how many times R U repeats before the cube is solved again. It prints: R U repeats 15 times on a 2x2 before the cube is solved again

Which Python ideas does it use?

lists, permutations, while loop, maths. Confident level, suitable from about age 13.

How do I run it?

Press Run on this page. To run it on your own computer, install Python 3 and save the code in a file ending in .py. It prints the same thing.

What should I try next?

Count the repeats of R alone. What do you expect? Try three moves in a row, such as R, U and R again. Print the state after one R U to see the rearrangement.

Start a conversation

Want a teacher to guide the learning?

Tell us the learner's age and what they can already do, and we will suggest a starting point. A parent or guardian can make the enquiry.

Tell us the learner’s age or grade and goals
We’ll suggest a suitable class or learning path
We’ll confirm format, timing and fees with a parent or guardian

Play it, don't just read it

Write some code right now

Free games that need no sign-up. Pick one and play for five minutes.

All free games →

Pick a game

Today's maths challengeFive questions · the same for everyone today · keep your streak goingPlay