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The Sledgehammer

When playing the 'cube', the main challenge is that positioning one cubie can often result in other cubies becoming disarranged.

To tackle that issue many Algorithms are developed. But what algorithms really do not really solve the problem but just change the 'nature' of the problem'.
(In other words: algorithms help solve the problem of determining which rotations to execute to solve the cube, but they also create a new set of problems that need to be addressed. These include:
- the need to know all the necessary algorithms to solve the cube
- remember them,
- choose the right algorithm for the specific situation
Moreover, many of these algorithms are so complex that they seem like mysterious, incomprehensible formulas.

The 'DIY method proposes a slightly different approach in which, for the majority of cases, the use of an algorithm emerges as a logical consequence of the various possible moves. In fact, you will see that in many cases, non-optimal moves will be chosen as long as the resulting algorithm is always the same: the sledgehammer. (When the user is able to independently identify better moves, that will be the signal that this tutorial has achieved its purpose.)

In the more complex cases (usually towards the end.) the sledgehammer will be used for its general properties:
- Swapping between two cubies
- Rotating the stickers on a cubie
- Rotating the edges
(These properties will be described later using 3D models.)

The sledgehammer was chosen for its simplicity and because it adapts well to the two different operational methods described above.
Algorithm as a "logical consequence": When positioning a cubie, it is necessary to move other pieces, but this has the effect of moving other cubies, which in turn requires correcting the undesired effects. Therefore, it was necessary to identify a set of moves for which:
- The 1st move (rotation) performs the action we want: that is the 'action move'
- The 2nd move is intended to protect the cubie just placed: that is the 'protection move'
- The 3rd move rolls back the side effect of the first move.
- The 4th move rolls back the side effect of the second move.

This sequence of moves generates 2 different algorithms

Sledgehammer
Sexy move

(Despite the fact the two algorithms are perfectly equivalent, this tutorial will use always the 'sledgehammer', even when is pretty clear the 'sexy move' is a better option. The reason is to keep as much simple as possible this tutorial following always the same way to do things. )
F R' F' R F R F' R'

The second rotation has the opposite direction of the first one (like 2 gears).
(This is the algorithm used here. )

The second rotation has the same direction of the first one (like the weels of a bicicle).
(This is the most used algorithm.)


Both cubes show only the cubies affected by its own algorithm

Properties

SWAP

Each time a sledgehammer is executed corners are swapped.

F R' F' R F R' F' R

Each 'sledgehammer, the corner Red-Yellow-Blue swaps its position with the corner Red-White-Blue.

Each 'sledgehammer, the corner Orange-Yellow-Blue swaps its position with the corner Gren-White-Blue.

ROTATION

Each time a sledgehammer is executed edges rotate.

F R' F' R

Each sledgehammer moves each edge to the place of one of the two neighbouring edges.

6 Sledgehammer

One "sledgehammer" involves cubies on 3 faces. (Red; Yellow; Blue in the example)

The same set of cubies can be moved by 6 different 'sledgehammers'.

The first rotation is optional; the remaining 3 are logically constrained.

1) R U' R' U (rollbacks the 'sledgehammer' 4.)
2) R' F R F' (rollbacks the 'sledgehammer' 5.)
 
3) U F' U' F (rollbacks the 'sledgehammer' 6.)
4) U' R U R' (rollbacks the 'sledgehammer' 1.)
 
5) F R' F' R (rollbacks the 'sledgehammer' 2.)
6) F' U F U' (rollbacks the 'sledgehammer' 3.)

CONCLUSION


Then:
- 1st 'sledgehammer' swaps corner. The edges rotate 1/3 of a turn.
- 2nd all corners return to their position but rotated. The edges rotate 2/3 of a turn.
- 3rd corners again swapped, All the edges returned to their place correctly oriented.
- 4th all corners return to their position but rotated. The edges rotate 1/3 of a turn.
- 5th corners again swapped, All the edges rotate 2/3 of a turn.
- 6th All the cubies are returned to their places and correctly oriented.