# Parity error prediction - and new simulator



## peterbone (Jun 22, 2006)

Is there a way to work out if a 4x4x4 cube is in the state of parity error? Maybe by counting how many edge pieces need rotating or something?

By the way, I've made a rubik's simulator you may like to try (free). It uses a 3D interface and you can set the size from 2x2x2 to 20x20x20 (will be slow on 20). I'll let you work out how to control it as it's pretty obvious but I will say that you can hold down ctrl while rotating a layer to rotate groups of layers - for 4x4x4 and higher. I'm actually faster at solving the 3x3x3 on the simulation that on a real cube - I'm not very fast. You can save the cube state, change the colours, etc. The biggest I've solved on it is 12x12x12.

http://star.walagata.com/w/peterbone/rubix.zip

Peter Bone


----------



## cmhardw (Jun 22, 2006)

Yes you can predict the parity error. With enough practice, it's possible even to never have the parity error at the end of your solve.

What you need to do is to follow the cycles of the edges as you mentally pair them up with their other edge piece to form an edge group. Do this during the initial inspection time. When you do this, make sure that you are creating edge groups that are already correctly oriented (in the 3x3x3 sense). When you have done this, see if your cycle is even (an odd number of pieces in it), or odd (an even number of pieces in it).

If your cycle is even then you must solve the cube with an even number of inner quarter turns. If the cycle is odd you must solve the cube with an odd number of quarter turns.

Solving in an even or odd number of inner face quarter turns is not very hard, I've practiced with it and I think it could be done very fast an average.

The hard part is that it is very difficult to count the cycles and determine the parity error within 15 second inspection time in a competition. The fastest I've ever counted the cycles was in under 30 seconds, I believe maybe around 26-29 seconds.

Anyway, not sure if this is what you were expecting as an answer, but yes it is absolutely possible to not only predict the parity error, but to avoid it 100% of the time. The only problem is that doing this in a competition in 15 seconds of inspection is extraordinarily difficult.

Chris


----------



## mrCage (Jun 25, 2006)

Hi 

This has been discussed quite a lot in the yahoo speedsolving group  

Personally i think it is possible to avoid the orientation parity by counting cycles or by other (simpler?) means. However i don't think it can be prodictive. For the normal pairing up/centers first approach i think inspection should be spent on studying centers so as to get a flying start with them. I don't think it is possible by inspection to avoid both orientation and permutation parities. So it is in my opinion more productive to learn algs dealing with both parities in one go, and learn how to detect what parities that occur quite early after doing centers and pairing (most of) the edges. But as already mentioned, this is my personal belief only  

Now about ur cube simulation. There must be a bug in it somehow, cause when i select pure white color for a face it will instead show as grey  I hope u can fix this as otherwise the simulation looks really cool  

Best wishes,

Per


----------



## mrCage (Jun 25, 2006)

Hi Peter  

I turned off the lighting. Then the white color shows properly. I still think it's a bug though. I really like this program. Gonna use this to practice 6x6x6 instead of the Gabbasoft one.

Cheers!

-Per


----------



## peterbone (Jun 26, 2006)

Thanks for your replies about parity. My reason for asking was indeed to avoid the parity error completely - I can see how the counting method would take a long time - longer than the parity error solve.

Glad you like the program. It's not a bug but I can see how it's a little annoying. I wrote the 3D graphics part myself from scratch and the lighting model is very simple. All the colours have the same intensity determined by the direction they face relative to the light source. In real life the white would obviously have a higher intensity. Maybe I could make it so that the intensity is altered above and below the intensity of the original colour rather than all the intensities being the same. I'll have a think about it - there are a few other things I need to improve too.

[edit] http://star.walagata.com/w/peterbone/rubix.zip Any better?


----------



## MasterofRubix (Aug 20, 2006)

Is it possible that when solving a super cube, you don't encounter any parities at all? It's a theory I want to test out but since I don't have a super cube, can anyone please tell me.


----------



## Johannes91 (Aug 20, 2006)

It's possible to swap two edges on a 4x4 super cube leaving everything else solved, for example.


----------

