6x6x6 Subgroup

This puzzle is a subgroup of the 6x6x6 group generated by allowing only 180-degree rotations along the center cuts for the XY and XZ planes, while allowing any 90 degree rotation about any of the YZ planes. (Of course, this idea generalizes to any NxNxN where N is even.) What you get is a scramble of the 6x6x6 into a bunch of 3x3x1 blocks. I will just refer to these as "blocks" for short.

Note that after a scramble under the constraints given above, performing random 90-degree rotations of all center planar cuts makes the puzzle a bit funner to solve. Just remember that no 3x3x1 block should ever be broken.

Step 1

Solve the 8 outer blocks on the left and right sides. It's easy.

Step 2

Now solve any 4 inner blocks that reside all on a single edge of the cube. It's also easy.

Step 3

The crux of the puzzle is now to position and orient the remaining 12 blocks. Begin by positioning and orienting all blocks for a single edge adjacent to the edge solved in step 2 using the penta-cycle Q1=R*,2U,R*i,2U and its symmetric equivilent Q2=L*i,2U,L*,2U.

Step 4

With 2 inner edges solved, only 8 blocks remain to be positioned and oriented. Try to position them with the quad-cycle Q3=2R*,2U,R*,2U,2R*. If this is not possible, I quad-cycle them into a case where just 2 need to swap in a single layer. I then rotate that layer 90-degrees to position one of them. This leaves 3 blocks mis-positioned in the layer. I then use Q1 and Q2 to position everything else in that layer and the mirror-image layer.

Step 5

All that remains is to orient the 8 remaining blocks. The sequence Q1,2Q2,Q1,Q3 will flip 3 pair of blocks at a time across 3 edges of the cube. Once you have it figured out, it's not hard to see how three applications of it, each from the appropriate perspective, will flip just a 1 pair of blocks; or how two applications will flip just 2 pair of blocks.