## Monday, January 4, 2010

### Edge Piece Series

Pick up your cube and look at any corner. Surrounding that corner will be 3 edge pieces. For instance, on a solved cube where white is opposite yellow and red is opposite orange, look at the red-yellow-blue corner. Surrounding that corner are the edge pieces

• top edge yellow-blue
• top edge yellow-red
• center edge blue-red

These three edges can be labelled as 1, 2 and 3 in six different ways. Here's 1 of the 6 ways:

Now, when we apply an Edge Piece Series (EPS) to this cube, things change.

To do an Edge Piece Series,
• Piece 1 replaces piece 2
• Piece 3 replaces piece 1
• Reverse move 1
• Reverse move 2

Let's see it step by step

Piece 1 replaces piece 2

Piece 3 replaces piece 1: notice that it replaces piece 1 where piece 1 is currently, not where piece 1 started

Reverse move 1

Reverse move 2
In standard notation, what we've done is U' R U R'

It's completely symmetrical, and the last 2 moves are just the reverse of the first 2 moves. But I encourage you not to think of it as U' R U R'. Instead, just think
• 1 replaces 2
• 3 replaces 1
• reverse move 1
• reverse move 2

Notice also that
1. piece 1 has replaced piece 2
2. piece 2 has replaced piece 3
3. piece 3 has replaced piece 1
4. the only edge pieces which have moved are the labelled edge pieces. All other edge pieces remain where they were
5. three corners on the front face have moved, and one on the right face, but none of the others have
6. piece 1 & 2 have kept their orientation but piece 3 has changed its orientation

Now, let's try the same thing with pieces 1, 2 and 3 in different starting positions.

1 replaces 2
3 replaces 1
reverse move 1

reverse move 2

Notice again that
1. piece 1 has replaced piece 2
2. piece 2 has replaced piece 3
3. piece 3 has replaced piece 1
4. the only edge pieces which have moved are the labelled edge pieces
5. three corners on the front face have moved, and one on the right face, but none of the others have
6. piece 1 & 2 have kept their orientation but piece 3 has changed its orientation
In fact, we can now summarise the EPS as follows.

Edge Piece Series

When we have 3 edge pieces surrounding a corner piece, we can apply an EPS choosing whichever pieces we like to be pieces 1, 2 and 3. The result will be
• 1 replaces 2 and keeps its orientation
• 2 replaces 3 and keeps its orientation
• 3 replaces 1 and changes its orientation

You will also have noticed that none of the bottom edge pieces were moved. This will come in handy.

Here's a video detailing the EPS

***** HERE'S ANOTHER MORE EXTENDED VIDEO ON THE EDGE PIECE SERIES *****

For completeness, here are the other 4 possible ways of labelling the edge pieces 1, 2 and 3.

Next, learn about the Corner Piece Series.

1. I've worked this out. I've completed the eps a number of times. Each time I focused on one edge piece and it helped me to see where it goes. This also helped me to see where edge piece 3 changes its orientation, yet the other two retain theirs.
Thanks!

3. @Anonymous,

Sorry, no. The point of Marshall's method was to make it doable without needing to resort to notation. If you look carefully, I do use notation once or twice above, but I agree with Marshall that the less notation to remember, the better.

4. After finishing reading this site I agree.

5. What a fantastic translational series on your blog THANK YOU!!! All from a webpage I myself tried reading a few years ago and found very difficult to follow.
You have reminded me of a short account of Edmond Halley and Sir Isaac Newton, in which Newton writes his most famous work and Halley goes about making it accessible to the masses. Great work, and good advice to anonymous, it does make more sense to think of it in the way you both suggest, here here!

1. Hey Claire

Thanks a lot! I remember spending a *lot* of time reading over and over Marshall's page until I "got it". The endgame for corners took the most time! Anyway, I'm glad you like it. Make sure you let your friends know about the blog, channel and FB page. Thanks again

6. Yep, this is clearer - but I'm stuck on the last 2 edge pieces. I'll head for the corners and have a look see if that helps