Sunday, September 9, 2012

2x3x4 Cuboid


The 2x3x4 Cuboid is a twisty puzzle whose solve has a few challenges, but I trust this tutorial will make things very simple. Please make sure you go through the whole tutorial.

The Basic Plot

  1. Return to cuboid shape.
  2. Attach the outer pieces to inner pieces.
  3. Solve the reduced 2x2x3.
Step 1: Return to Cuboid Shape

Before looking at how to return to cuboid shape, let's see the main sequence involved in this solve. It's the corner piece series for cuboids, which basically means that our left and right sides are turned 180° instead of 90°.



Returning to cuboid shape is not difficult. We can use simple turns, or else employ the corner piece series. This video shows a number of different scenarios and how to deal with them.



Step 2: Attach Outer Pieces to Inner Pieces

The first part of this step is quick and simple. We simply turn the left or right faces to make sure that the edges are attached correctly.


The second part of this step is where the challenge comes. Rather than resort to a longer commutator (which is perfectly possible, and which you can see in action on my 3x4x5 videos) I have included in this tutorial several different approaches to solving the puzzle simply.

Once the edges are reduced, there can be anywhere from 0 to 5 corners reduced as well. I have included 4 example videos below, which show the sorts of approaches we can take. You will find that once you see what's going on, you'll be able to figure out any other situations that arise.

Sometimes the reduction will proceed by using only edge piece series, with the puzzle always remaining in cuboid form. At other times, we will need to employ corner piece series. When this happens, the puzzle will become shapeshifted, but we will return it to cuboid form by the end.

Example 1
We can place 2 reduced corners together at down-right, and then carry out a single edge piece series to complete the remaining corners.


Example 2

To begin with, no corners are reduced. We try simple twists but nothing changes. We carry out an edge piece series. Now, two corners are done, which leads to the same outcome as above.


Example 3

We find four already-reduced corners in the same orbit (as in, each corner can be turned into the position of the others while remaining in cuboid form). We carry out an edge piece series. This leads to four reduced corners which are not in the same orbit, and which are next to each other. We place all four on the right hand side. One turn of the left face and all corners are reduced.


Example 4

We find four already-reduced corners which are not in the same orbit (this means we cannot turn each corner into the other positions without going to cuboid form). We carry out a corner piece series. This shapeshifts the puzzle, and leads to four reduced corners which are next to each other. (We shapeshift again using 3 different unreduced corners to return to cuboid shape.) We place all four reduced corners on the right hand side. One turn of the left face and all corners are reduced.




Step 3: Solve Reduced 2x2x3


At this point, all outer pieces are attached to their inner pieces. We now solve the puzzle as though it were a 2x2x3 cuboid. We make sure to always turn both left layers or both right layers, so as not to undo our attaching work above.The edges are solved first using simple turns. Then the corners are solved using simple turns or corner piece series. When we carry out a corner piece series, the puzzle will become shapeshifted, but it will always return to the cuboid form once it's solved.


Help! I Have Two Corners Which Need To Swap!

It is of course possible to end up with two corners needing to swap, just as it is on the 2x2x3. If this happens, turn the upper or lower face one turn, then re-solve the corners using the corner piece series.

This final video will show how to deal with two swapped corners at the end.




And that's it. Your 2x3x4 Cuboid 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.


1 comment:

  1. Awesome! Had a quick scan only - I want to see if I can do it myself with my own techniques and then try yours! I didn't think it would take you long!

    I'm still struggling to put the replacement parts from Calvin back inside and close it up. Hopefully soon!

    Kevin
    Puzzlemad

    ReplyDelete