# Thread: Devil Algorithm for 2x2x2 (R U moves)

1. ## Devil Algorithm for 2x2x2 (R U moves)

Today I found Devil's Algorithm (Hamiltonian Cycle) for bandaged 2x2x2 cube (only R U moves). Finally!

http://cubemir.ru/speedcubing/222/Devil_222RU.txt

There are 29160 positions in bandaged 2x2, and this alg goes through every position, but never pass through the position where it already was. So it is 29159 moves long. 29160th move returns the cube in solved state, so it is cycle.

Next time I'll try to find Devils Alg for 2x2x2 (3674160 positions). But it will be much more harder...

2. Wow, how did you find it? Brute force?

3. Crazy.
Awesome job!

4. Originally Posted by Owen
Wow, how did you find it? Brute force?
Of course I used a bit of a computer

5. Great job, though don't you mean bandaged, not bondaged?

6. So basically it's just every 2x2 position with a 2x1 block solved?

Absolutely amazing though, I'm surprised somebody found this on a desktop(?) computer. Now to find Devil's Alg for all of 2x2! Then 3x3 (that'll be interesting)

7. Originally Posted by theZcuber
So basically it's just every 2x2 position with a 2x1 block solved?

Absolutely amazing though, I'm surprised somebody found this on a desktop(?) computer. Now to find Devil's Alg for all of 2x2! Then 3x3 (that'll be interesting)
Thanks, but I see cuBerBruce has already found Hamiltonian circuit for all 2x2 positions. But never mind I'll try to find my own one

8. Originally Posted by theZcuber
So basically it's just every 2x2 position with a 2x1 block solved?
Not quite. There are many 2x2x2 scrambles that have a 2x1x1 block solved can't be reached by only applying <R,U> moves. This only solves the ones that can be reached with <R,U>

9. Very cool stuff!

10. Originally Posted by theZcuber
Then 3x3 (that'll be interesting)
Good luck storing that on your computer :P

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