## Saturday, March 16, 2013

### 7x7x5

The 7x7x5 is a twisty puzzle which is a cuboid when solved, but which can shapeshift when scrambled. The one I'm using is a beautiful handmade version made by Traiphum. It is an absolutely superb puzzle.

The Basic Plot

1. Return to Cuboid Shape
2. Solve the Centers
3. Reduce the Edges
4. Solve the Reduced Cuboid
Step 1: Reduce to Cuboid Shape

The first stage in solving this puzzle is to return it to a cuboid form, rather than shapeshifted form. To do this simply, we will make use of the corner piece series for cuboids. This sequence is (U R2 U' L2) x 2, but it has many variants according to which slices are turned.

Here are the steps which form the basic solve outline...

1. Solve the 3x3 centers on the white/yellow faces.
2. Make white/yellow edge triplets according to piece type, not colour.
3. Make a horizontal row of middle face center triplets.
4. Flatten the 2nd slice pieces.
5. Flatten the outer slice pieces.
6. Move middle layer pieces on the top and bottom faces into the middle layer.
7. Check that all middle layer edges are correctly oriented. If not, flip them, using a double EPS.

By now, the puzzle will be in correctly reduced cuboid form.

If the above steps seem difficult, they are not. Please watch the video below where I go through all the above and (hopefully) make things very clear and simple.

Step 2: Solve Centers

We now have a scrambled but non-shapeshifted 7x7x5.

The next step is to solve the centers. Start with the white/yellow centers, using the corner piece series variants to place the different piece types.

To solve the middle centers, make quintets of inner layer "edges". This is done just as we'll do it for the outer edges later. Once they're made, the white/yellow centers will be disrupted. So we move the newly made middle layer quintets onto another face, then return centers. The process is analogous to that done on a 7x7x7.

Step 3: Reduce Edges

To reduce the edges, follow the same procedure as above, but this time turn the outer face only on top and bottom.

The interesting part of this solve is the parity case which often occurs. This will only occur when the puzzle has returned from a shapeshifted form. It shows up when the final two edge pieces need to swap. It is not possible to fix this without either a long-and-hard-to-memorise algorithm, or else a way of understanding what's going on and working from there. I choose to avoid the algorithm.

Step 4: Solve the Reduced Cuboid

At this point, we have reduced the puzzle to what is essentially a 3x3x2. To complete the solve, we

1. Place the middle outer edges.
2. Place the middle outer "corners".
3. Place the edge quintets.
4. Place the corners.
All of this is done using simple turns and of course, the corner piece series. It's pure relief after the slog to get to this point.

This video will show the process.

And that's it. Your 7x7x5 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. I'm so glad you've enjoyed this puzzle!
After the 3x5x7 it's my absolute favourite.

Kevin
Puzzlemad