## Sunday, October 6, 2013

### 3x3x5 by Reduction

The 3x3x5 Cuboid is a twisty puzzle where the standard 3x3x3 cube has had a face attached to top and bottom. This cuboid shapeshifts, due to the 3x5 face. I'll be solving this cube using a reduction method, which I think is the simplest method to solve it. To buy this puzzle, click here.

The Basic Plot
2. Reduce Edges and Corners
3. Solve Reduced Cuboid

To begin with, place the orange and red edges. We don't need to solve them as such, just put the edges into an edge position. This involves nothing more than simple turns. Once the edges are placed, we can place the unreduced corners, which are currently sticking out all over the place, by using the corner piece series for cuboids. This is

(U R2 U' L2) x2

This process will flatten the sticking-out corners and return our puzzle to cuboid shape.

2. Reduce Edges and Corners

The first stage of the reduction is to attach the outer edge pieces to a corresponding inner edge colour. This is done by using the edge piece series, such as U F2 U' F2.

Once all edges are reduced, we reduce the corners. This also uses the corner piece series as above, and cycles UBL->DFL->DFR.

If we find there are two corners remaining which need to be reduced, this means we have a single swap of corners, but no swaps of edges. In order to fix this problem, we turn the upper face one turn. This creates a single swap of edges and no swap of corners. But we can easily re-reduce our edges using the edge piece series. This process will therefore mean that we will have a 3-cycle of corners at the end.

3. Solve Reduced Cuboid

Stage 3 is probably the simplest stage of the solve.

First, we use simple turns to place the middle layer edges.

If simple turns won't do, then we need to swap (or flip - or both) two middle layer edges. The video below shows how to accomplish this.

Then solve the reduced edges and corners exactly as for a 3x3x2 cuboid, ignoring the middle layer.

As with a 3x3x2, it's possible to end up with two reduced edges needing to swap. The fix for this is to turn both the upper two layers one turn, then resolve the reduced edges.

And that's it. Your 3x3x5 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.

1. Thanks again for another great tutorial!!! In a lot of the solves using this method I ended up with a swap of two middle layer edges (the third slice). Anyway of solving this problem? Thanks

2. Just seen similar comments to mine on your youtube channel. You posted a video showing a fix but the link doesn't work for me. Could you repost it? Thanks

1. Hi Beasty
The 1st problem was the videos weren't showing. Youtube change there unerlying code and my videos don't show. I've fixed that now. I'm still not clear on which other video you can't see the link to.