? Step Five

# The Ultimate Solution to a 3x3x3x3

## Step Five:  Four-Colored Corner Pieces

When you are done with the edge pieces, you can begin to see the end of this long process.  It doesn?t seem so far now, huh?  Here is the hypercube with only the corners left to solve and first corner piece to solve labeled #1.

To place the corner pieces on the hypercube, we are going to have as tools two new Four-Color Series.

The First Four-Color Series

The Second Four-Color Series

You can read descriptions of those series and their corresponding moves below.  There are 16 corner pieces that we need to solve using these series.

The idea behind applying these sequences is the same as we used in solving the edge pieces.  The First Four-Color Series will shuffle around 3 corner pieces without disturbing any edge or face pieces.  This is the series you will use most often.  The Second Four-Color Series is used to flip a single corner piece in cases where you need to do this.

Almost always, the First Four-Color Series will not move a piece into its correct position and orientation without some preliminary moves.  At this stage in the game, we are often required to do more preliminary moves to place pieces.  Luckily, though, by now you have had a fair amount of experience manipulating the cube and hopefully this is becoming more natural.

Since the process is so similar to the edges (really, only the Series applied is different), I will be brief with an example.  The pink/blue/red/cyan piece I have labeled #1, upon execution of the First Four-Color Series will move as follows:

 1a moves to: Left, 21 1b moves to: Back, 1 1c moves to: Top, 19 1d moves to: Upper, 25

But it belongs where the green/orange/purple/red piece is.  (It was necessary to do a 4D cntl-click rotation to see that the red place was in the ?cyan? position of where the #1 piece belongs).  Hence we want our preliminary moves to put the green/orange/purple/red piece into the positions above.  Luckily, this is a very simple scenario and requires only one preliminary move.

 Back, 15, Left

Executing the sequence, then undoing this preliminary move solves the #1 piece.  Continue in this manner to solve the rest of the corners one at a time.  Remember that just as required with the edges, when you have only 3 corners left to solve, you will need to solve them all at the same time.  This will require doing preliminary moves for two of the pieces instead of just one.

When you are done, save and send your log file to MagicCube4D@superliminal.com and get your name listed in the MagicCube4D Hall of Fame!