## Tuesday, March 13, 2012

### 3x4x5 Cuboid

The 3x4x5 Cuboid is a twisty puzzle in cuboid shape. It's not a particularly easy solve, but I trust this tutorial will help. It's a fairly long and involved tutorial, but it's deliberately done that way to help you solve the puzzle every time. Please make sure you go through the whole tutorial.

The Basic Plot
2. Reduce edges.
3. Reduce corners.
4. Solve the edges on the reduced 3x3x4.
5. Solve the corners on the reduced 3x3x4.

This step is not strictly necessary but it makes life a lot easier. When returning to cuboid shape, we're not interested in where the pieces go, just so long as by the end, we have a cuboid.

To begin with, place two sets of 3x4 centers opposite each other. Then place edges into position using edge piece series. Finally, bring all other pieces back to cuboid shape using corner piece series.

Step 2: Reduce Edges

In this step, we hold the puzzle so that a 3x5 face is on top and a 4x5 face is at front.

First, attach the edge pieces. This is a simple step and lulls us into a false sense of achievement about this puzzle.

Next, we want to focus on the two inner layers between the up and down faces. Looking at the front face, we see there are 5 pieces horizontally. We're not concerned with the center piece. On either side of the center are two other pieces: an inner piece with only one colour, and an outer piece which has two colours. Our job is to attach an outer piece to an inner piece so that their colours match. We also need to do this without disturbing the edges we've already attached.

To do this, we'll use a sequence involving the corner piece series. This sequence cycles 3 of the outer pieces and moves them onto the required inner pieces. In this way, we normally only have to carry out the sequence once or twice to attach all outer pieces to inner pieces in these central layers.

The sequence is

CPS clockwise    (F2 R2 F2)    U   CPS anticlockwise   U'    (F2 R2 F2)

It cycles the outer pieces FLD -> BRD -> BLU.

When we do the corner piece series, we need to turn the 2nd upper layer rather than only the top upper layer.

IMPORTANT NOTE: This puzzle sometimes blocks. That means that when you go to turn either the right or left face, it won't turn. This is purely an issue with the 3x4x5 puzzle. It happens on the mass-produced versions as well as the custom-made ones. There is a way to unblock the sides (thanks to Burgo from Twisty Puzzle forums!) and I include it here as you'll sometimes encounter a blocked side in the sequence above.

To unblock an R2 turn, do

Uu2 Ll2 Uu Ll2 Uu2 (to unblock)
R2
Uu2 Ll2 U'u' Ll2 Uu2 (to return the puzzle to where it was before you unblocked it)

To unblock a L2 turn, do

Uu2 Rr2 U'u' Rr2 Uu2 (to unblock)
L2
Uu2 Rr2 Uu Rr2 Uu2 (to return the puzzle to where it was before you unblocked it)

Now that we've gone through that, have a look at this video. It shows how to attach the outer pieces to the inner pieces. Also in this video is an example of blocking and how to get around it following what's written above.

Step 3: Reduce Corners

At this point, we have all edges attached and all pieces in the central two layers attached. All that's remaining is to attach the outer corners to the inner corners on the up and down faces.

We do this in the same way as for the central layers, except that when we turn the upper face, we only turn the top upper face (not both the top and the 2nd).

Again, the sequence is

CPS clockwise    (F2 R2 F2)    U   CPS anticlockwise   U'    (F2 R2 F2)

It cycles the outer corners FLD -> BRD -> BLU.

There are two cases which you may encounter during the solve.

Case 1: The corners can be attached simply by using the sequence above.

When this happens, we carry out the sequence above 1-3 times, depending on how many corners need attaching.

Case 2: The corners are in a 2+2 swap formation and cannot be attached just by using the sequence above. This means that of the 4 corners remaining, one set of 2 corners need to swap and the other set of 2 corners also need to swap. To get out of this situation, we need to turn either the left or right face, to "break" the problem, and then re-solve the other parts. It's not difficult, just a little time consuming.

This video explains all.

Step 4: Solve Edges of Reduced 3x3x4

At this point, all outer pieces are attached to their inner pieces. We now solve the puzzle as though it were a 3x3x4 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 or edge piece series.

Step 5: Solve Corners of Reduced 3x3x4

The corners on the inner 3x5x2 are solved first. Do this just as if you were solving the inner part of a 3x3x4. The puzzle will leave cuboid shape while doing this but will always return at the end.

If you need to swap two of these corners, proceed exactly as for a normal 3x3x4. Turn the upper face one turn, then re-solve the edges, then re-solve the corners.

Now, the only thing remaining is the reduced corners on the up and down faces. Again, proceed as for a 3x3x4.

And finally, if you need to swap two of these corners, proceed as for a 3x3x4. Turn the upper face one turn, then re-solve the inner corners, then re-solve the edges, then re-solve the corners.

This video will explain all.

And that's it. Your 3x4x5 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. Awesome! Way beyond my capabilities - I think I am going to have to go back to the basics again and see if I can figure it out.

I do actually have this puzzle on the way but suspect I will have to master a few others first.

Kevin