Sunday, October 20, 2013

Curvy Copter tutorial! (No jumbling)

Welcome to TheCubingKyle's Curvy Copter Tutorial!
Buy this puzzle Here

First things first, we should define our notation for the algorithms that we're going to use. All turns are of 180 degrees, and most of it is intuitive so this is only important for the last layer. Thus we are only naming the top edges with L for left, B for back, R for right, and F for front. The pieces are going to be called corners (for the three-colored corners), Petals (For the single-colored curved triangular inner bits) and edges (For the diamond shaped, two-colored pieces).

This tutorial is not going to deal with the jumbling until I can find a nice way of phrasing everything.

A few disclaimers before we start the solve: 
  • I do not own a high quality camera and apologize for that. You'll just have to believe me when I say the stickers are actually the color I say they are.
  • As the subtext above says, this tutorial is not for jumbling. I'll be appending this with a jumbling explanation if it is requested. There are currently plenty of jumbling explanations.
  • This is just a series of pictures, not a video, so I've only shown one example of each stage instead of the placing of every piece in an effort to shorten it.
  • I do not know every Curvy Copter method out there, this is just how I solve it and I am sure it bears similarities to other methods. I assure you I am not stealing intellectual property.
  • This is my first post and welcome ALL criticisms, critiques, requests, and suggestions.
Let's get started, shall we?

Step 1: Solving edges of one face. For this tutorial I'm using white. The first step is to locate four white edges. I turned them all up for this picture, but we want them all turned down to connect petals to them.

 If there is a petal on the top when all the edges are turned down, turn the petal it is connected to, turn an adjacent edge piece, then undo those moves (R,B,R,B for example)

Placing the petals is none too difficult. Here we can turn this column (Which is any standing axis - four in all for each edge to the cube) to place to petals next to their respective edges. Take a moment to see what pieces your turn is affecting and it won't be hard to pair each petal to an edge. Turning them all up to the top face is equally intuitive. If you have trouble bringing them all up together, experiment with the same technique of turning an edge, an adjacent edge, then undoing these moves. Experimentation is good and helps you understand the puzzle.

This is what you want your top face to look like at the end.

Step 2: Block building the side columns. The first step is to line one corner up underneath its edge upside down, so that once the block is built we can turn it up to place it, and we're doing this one at a time.
Turn a corner underneath the edge it belongs to (Green orange white corner belongs to the green orange edge) using simple bottom layer turns. If there is no corner in the bottom, turn one into the bottom.
Remember, we are building these blocks upside down. The corners will eventually end up on the top, but we build them with the top color facing downward.

Don't fret if your corner is not oriented. Look at the color that will end up on bottom (top in the end). Cycle the corner around the bottom layer in the direction of that color. In this example, we want white on bottom and white is facing clockwise, so we will cycle it clockwise to align it.


When not jumbling there are only certain "orbits" a petal can be in for placing. You can use your eyes to follow where an edge would go if you turned any adjacent edge. This picture shows the first three positions a petal can possibly be in, but you can use your eyes to follow an edge all the way around the puzzle.
The green petal in position 1 is one turn away from position 2, from then to position 3, and etc. There are 5 positions it can be in without disrupting the top petals.

This is the position we want the petal to be in for placing, position 3. It is one turn away from being nestled between its corner and edge, like the orange one is.

However, turning it directly in would disrupt the corners, so this series of moves will protect the corner, edge, and already placed petals.
Turn the corner away from the edge that needs to be placed (this edge is placing on the left, so turn the corner off to the right).

Place the edge.

Turn the corner back on.

If done correctly, the petal will be placed. Once you have an edge above a correct corner, and its two adjacent petals built into a block, turn it up.

What if my edge is in position 1, above the corner?
Here, the upper red piece needs to be turned down into place - but won't that wreck my edge/corner pair?

All you have to do is follow a few extra steps I have listed below!
Turn the petal down into position. Remember, its final position is diagonal from where it started in the column.

Turn the petal off of the column toward the direction it will be placed. This red piece needs to be on the right, so it's being turned right.

Turn the column back so that the corner is on the bottom again, and your petal is in position 3, which is gone over below once again.

Turn the corner away from the edge that needs to be placed (this edge is placing on the right, so turn the corner off to the left).

Place the edge.

Turn the corner back on.

Using these two simple methods you can place all the corners of the top layer, the middle edge pieces, and half of the middle petals. All of the unplaced pieces are now in the bottom orbits so let's flip this puzzle over and work on what from now on is the top!
Finished first half.

Step 3: Placing top Petals. This is another extremely intuitive step. As long as you are conscious of keeping the petals aligned with the correct color of their edges, it's usually a few self-obvious moves.

The reds are one turn away from solved, and will set up the blue petals to be solved.

After solving the blue petals, one turn of the orange edge will set up the green petals.

Now the green petals can be solved in one turn and set up the final, orange petals to be solved in one turn.

Tadaa! That's it. You've solved all of the top petals and edges, practically by accident.

Step 4: Permuting the top corners. The orientation of the corners doesn't matter. I just oriented them first to make this 3-cycle more visible.

In this 3-cycle, the back right corner is unaffected, the front right corner moves to the front left, front left to back left, and back left to front right. This counter clockwise 3-cycle is shown in the picture below.

Here comes our first actual algorithm (yay!) to perform this 3-cycle, simply execute (R,B,R,F)x2. The clockwise version, in which the front left corner needs to move to the front right position, is (F,R,B,R)x2.

What if no corners are in? Just perform a 3-cycle and one should place.


Step 5: Orienting Corners (endgame). Well, everything is now where it should be. The only thing we haven't done is twisted a few corners. Below is a picture of what I consider the main case, as it's what I developed my algorithm off of. The algorithm for this is (R,L,B,R,L,F)x2. Seeing as none of the pieces of R or L intersect and one is after the other, they can be done in either order. Essentially it's (Both sides, back, both sides, front)x2.

Here is this case's inverse. To solve it, just reverse the commutator used and perform (F,R,L,B,R,L)x2.

What if I have three corners out? Well, orient your puzzle so that two of them are in the front, and one is in the back right. Perform whatever of the two algorithms would solve the front left corner.
In this case, it is (F,R,L,B,R,L)x2.

After doing this, you will have two adjacent corners that falls under either case 1 or case 2.

What if my two corners are not adjacent? Position the corners so that one is in front left, and the other is in back right. Execute the algorithm that will solve the front left, and you will be left with either case one or case 2.

What if I have 4 misoriented corners? This will always create two pairs of either case 1 or case 2.

And You've Done It!
Through effort, will, and cunning, and your inexplicable ability to follow my terrible instructions, your Curvy Copter is now solved. Once again, I invite and encourage all criticism, critique, request, or suggestion and I will do my best to respond with aid. Thanks all who used or at least read this and I hope to provide you with more posts soon!

8 comments:

  1. Welcome to the blogging world! Nicely written first post.

    Take it slow and do what you love! That way you'll keep going for a long time.

    Kevin
    Puzzlemad

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    1. Hey thanks Kevin :) I'm still figuring out how to format this so it's not hard to look at but I just hope my content is well enough for now

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  2. Hello, great tutorial! I always ended up with two corners twisted and I would scramble the top part and do it again and now You taught me! Great

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    1. Awesome! I now consider this tutorial a success! I think my top layer is where I differ most from other methods.

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  3. I like your corner orientation algorithm. I do (R B L F) x 6 to rotate 3 corners. Your method is quicker.

    One suggestion for a future topic - how you approach a new puzzle and find algorithms for it.

    Kevin
    Puzzlemad

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    Replies
    1. Our algorithms are the same move count :p is it just that mine is easier to execute? I'll tackle that along with how I got into twisty puzzles, because they are very tied together

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    2. Mine is 24 moves vs yours at 12!
      Mine is very easy to remember but not elegant at all.

      I look forward to the history too!

      Kevin
      Puzzlemad

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    3. What I mean is it takes 24 moves to rotate three with my method :) But I think mine is better since two-corner cases are more common

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