Sunday, November 4, 2012

4x4x4 AI Bandaged Cube

The 4x4x4 AI Bandaged Cube is a bandaged twisty puzzle in the shape of a cube. It has each of the four diagonally opposite corners bandaged in a 2x2x2 block. All other pieces are single cubies.

I have no idea why this puzzle is referred to as "AI". If you know, tell me in the comments.

To buy this puzzle, click here.

The Basic Plot

1. Reduce the 1st 2x2x2 block.
2. Reduce the 2nd block.
3. Reduce the 3rd block.
4. Reduce the 4th block.
5. Solve the reduced 2x2x2.
Step 1: Reduce the 1st 2x2x2 Block

Before we begin, feel free to watch this preliminary video, where I tell you why my cube doesn't look like the official one, and explain a few other things about the sequence we'll use.

Reducing the 1st block is by far the easiest step (apart from the final solve of the reduced blocks).

We first make a center-edge-center triple and store it on the lower layer. We then have three unused blocks to create first our corner-edge pair, and then our remaining edge-center pair. Once you see how straightforward this step is, you'll realise that the remaining blocks are done in the same way but with more restrictions.

Step 2: Reduce the 2nd Block

Reducing the 2nd block is nearly as simple as the 1st. The principles are entirely the same.

Step 3: Reduce the 3rd Block

The 3rd block presents the challenge of having only two blocks to work with. We don't want to disrupt the already-reduced blocks. We proceed in the same way but we need to be more thoughtful about how we move our pieces around.

Sometimes, it seems impossible to correctly match up the last edge-center pair. When this happens, match the corner with that edge, and then the remaining edge-center pair will match easily.

This video shows both possibilities.

Step 4: Reduce the 4th Block

In reducing the 4th block, we have our biggest challenge. This step is hard!

I've come across six different cases for the state of the 4th block, and I present each of them here. It's not appropriate to give sequences here, because it all depends on which colour we're trying to match. but essentially, that's what we're doing with each case: matching the colours of edges and the corner with appropriate centers.

Case 1
Here, we have a corner-edge pair already made, but another edge unmatched with its center.

Case 2
Here, we have the corner in position, and three edge-center pairs needing to cycle around the corner.

Case 3
Here, everything is in place, except for three centers which need to cycle around the corner.

Case 4
Here, we have a twisted corner and two swapped centers.

Case 5
Here, we have everything in place, apart from three edges which need to cycle around the corner.

Case 6
In this final, and most difficult case, we have everything in place, except for the corner, which is twisted.

Step 5: Solve the Reduced 2x2x2

This is pure relief after the challenge of the 4th block. We now solve the reduced 2x2x2 blocks, by treating each of them as one corner on a 2x2x2 cube. The method is exactly the same.

And that's it. Your 4x4x4 AI Bandaged Cube is now solved. I trust this site has been helpful. If you have any questions or want some clarifications, please use the comments to do so. To buy this puzzle, click here.