The fix can be downloaded from its page on my web site.
February 6, 2009
February 3, 2009
How to Solve a Rubik's Cube
from wikiHow - The How to Manual That You Can Edit
The Rubik's Cube can be very frustrating and may seem next to impossible to restore to its original configuration. However, once you know a few algorithms, it is very easy to solve.
The method described in this article is the layer method: we first solve one face of the cube (first layer), then the middle layer, and finally the last layer.
Steps
- Familiarize yourself with the Notations.
- Choose one face to start with. In the examples that will follow, the color for the first layer is white.
- First Layer
- Solve the cross : place in their correct position the four edge pieces that contain white. You should be able to do this by yourself without needing algorithms. All four edge pieces can be placed in a maximum of 8 moves (5 or 6 in general).
- Place the cross at the bottom.
- Solve the four corners of the first layer, one by one. At the end of this step, the first layer should be complete, with a solid color (in this case, white) at the bottom. You should also be able to place the corners without needing algorithms. To get you started, here is an example of one corner being solved:
- Your cube should now have the first layer complete and look like this (from the bottom side) :
- Solve the cross : place in their correct position the four edge pieces that contain white. You should be able to do this by yourself without needing algorithms. All four edge pieces can be placed in a maximum of 8 moves (5 or 6 in general).
- Middle Layer
- Place the four edges of the middle layer, one by one. Those edge pieces are the ones that do not contain yellow in our example. You need to know only one algorithm to solve the middle layer. The second algorithm is symmetrical to the first.
- If the edge piece is located in the last layer : (1.a) (1.b)symmetrical to (1.a)
- If the edge piece is in the middle layer but in the wrong place or with the wrong orientation, simply use the same algorithm to place any other edge piece in its position. Your edge piece will then be in the last layer, and you just have to use the algorithm again to position it properly in the middle layer.
- If the edge piece is located in the last layer : (1.a) (1.b)symmetrical to (1.a)
- Your cube should now have the first two layers complete and look like this (from the bottom side) :
- Place the four edges of the middle layer, one by one. Those edge pieces are the ones that do not contain yellow in our example. You need to know only one algorithm to solve the middle layer. The second algorithm is symmetrical to the first.
- Last layer
- Permute the corners. At this step, our goal is to place the corners of the last layer in their correct position, regardless of their orientation.
- Locate two adjacent corners that share a color other than the color of the top layer (other than yellow in our case).
- Turn the top layer until these two corners are on the correct color side, facing you. For instance, if the two adjacent corners both contain red, turn the top layer until those two corners are on the red side of the cube. Note that on the other side, the two corners of the top layer will both contain the color of that side as well (orange in our example).
- Determine whether the two corners of the front side are in their correct position, and swap them if needed. In our example, the right side is green, and the left side is blue. Therefore the front corner on the right must contain green, and the front corner on the left must contain blue. If it is not the case, you will need to swap those two corners with the following algorithm: Swap 1 and 2 : (2.a)
- Do the same with the two corners at the back. Turn the cube around to place the other side (orange) in front of you. Swap the two front corners if needed.
- As an alternative, if you notice that both the front pair and the back pair of corners need to be swapped, you can do it with only one algorithm (note the huge similarity with the previous algorithm): Swap 1 and 3 : (2.b)
- Locate two adjacent corners that share a color other than the color of the top layer (other than yellow in our case).
- Orient the corners. Locate each top color facelet of the corners (yellow in our case). You need to know only one algorithm to orient the corners : (3.a) The algorithm will rotate 3 corners on themselves at once (from the side to the top). The blue arrows show which 3 corners you are turning, and in which direction (clockwise). If the yellow stickers are the way shown on the pictures and you perform the algorithm once, you should end up with the four yellow stickers on top : It is also convenient to use the symmetrical algorithm (here the red arrows are counter-clockwise turns): Symmetrical to (3.a) (3.b) Note : performing twice one of these algorithms is equivalent to performing the other.In some cases, you will need to perform the algorithm more than once :
- 2 correctly oriented corners : = = + = = + = = +
- no correctly oriented corner : = = + = = + Or more generally, apply (3.a) in those cases : Two correctly oriented corners : No correctly oriented corner :
- 2 correctly oriented corners : = = + = = + = = +
- Permute the edges. You will need to know only one algorithm for this step. Check whether one or several edges are already in the correct position (the orientation does not matter at this point).
- If all the edges are in their correct positions, you are done for this step.
- If one edge only is correctly positioned, use the following algorithm : (4.a) or its symmetrical : Symmetrical to (4.a) (4.b) Note : performing twice one of these algorithms is equivalent to performing the other.
- If all four edges are incorrectly positioned, perform one of the two algorithms once from any side. You will then have only one edge correctly positioned.
- If all the edges are in their correct positions, you are done for this step.
- Orient the edges. You will need to know two algorithms for that last step : Dedmore "H" Pattern (5) Dedmore "Fish" Pattern (6) Note the DOWN, LEFT, UP, RIGHT, sequence to most of the Dedmore "H" and "Fish" algorithms.Note you really have only one algorithm to remember since : (6) = + (5) + If all four edges are flipped, perform the "H" pattern algorithm from any side, and you will have to perform that algorithm one more time to solve the cube.
- Permute the corners. At this step, our goal is to place the corners of the last layer in their correct position, regardless of their orientation.
- Congratulations! Your cube should now be solved.
Tips
- Know the colors of your cube. You must know which color is opposite which, and the order of the colors around each face. For instance, if white is on top and red in front, then you must know that blue is on the right, orange in the back, green on the left and yellow at the bottom.
- For the color to start with, you can either always start with the same color to help you with knowing where each color goes, or try to be efficient by choosing a color for which it is easier to solve the cross.
- Practice! Spend some time with your cube to learn how to move pieces around. This is especially important when you are learning to solve the first layer.
- To solve the cross efficiently, first locate all four edges and try to think ahead about how to move them into position without actually doing it. With practice and experience, this will teach you ways to solve it in fewer moves. And in a competition, participants are given 15 seconds to inspect their cube before the timer starts.
- Try to figure out how the algorithms work. While executing the algorithm, try to follow key pieces around to see where they go. Try to find pattern in the algorithms. For instance :
- In the algorithms (2.a) and (2.b) used to permute corners of the last/top layer, you execute 4 moves (at the end of which all first/bottom layer and middle layer cubies are back in the first/bottom and middle layers), then turn the upper layer, and then execute the reverse of the first four moves. therefore this algorithm does not affect the first/bottom and middle layers.
- For the algorithms (4.a) and (4.b), note you are turning the top layer in the same direction that you need to turn the three edges.
- For the algorithm (5), Dedmore "H" Pattern, a way to remember the algorithm is to follow the path of the flipped edge on the top right and the pair of corners around it for the first half of the algorithm. And then for the other half of the algorithm, follow the other flipped edge and pair of corners. You'll notice that you perform 5 moves (7 moves if counting half turns as 2 moves), then half turn the top layer, then reverse those first five moves, and finally half turn the top layer again.
- In the algorithms (2.a) and (2.b) used to permute corners of the last/top layer, you execute 4 moves (at the end of which all first/bottom layer and middle layer cubies are back in the first/bottom and middle layers), then turn the upper layer, and then execute the reverse of the first four moves. therefore this algorithm does not affect the first/bottom and middle layers.
- Progress further. Once you know all the algorithms, you may want to find faster ways to solve the Rubik's:
- Solve the first layer corner along with its middle layer edge in one move.[1]
- Learn algorithms to orient the last layer corners in the five cases where two (3.a/b) algorithms are necessary.
- Learn algorithms to permute the last layer edges in the two cases where no edge is correctly positioned.
- Learn the algorithm for the case where all last layer edges are flipped.
- Solve the first layer corner along with its middle layer edge in one move.[1]
- Progress even further. For the last layer, if you want to solve the cube fast, you will need to do the last four steps two by two. For instance, permute and orient the corners in one step, then permute and orient the edges in one step. Or you can choose to orient all corners and edges in one step, then permute all corners and edges in one step.[2]
- The layer method is just one of many methods out there. For instance, the Petrus method, which solves the cube in fewer moves, consists in building a 2×2×2 block, then expanding it to a 2×2×3, correcting edge orientation, building a 2×3×3 (two layers solved), positioning the remaining corners, orienting those corners, and finally positioning the remaining edges.[3]
- For those interested in speed cubing, or those who simply don't like how hard it is to turn pieces, it is a good idea to buy a DIY kit. The pieces of speedcubes have rounder inner corners and DIY kits allow you to adjust the tension, making it a lot easier to move pieces. Consider also lubricating your cube with a silicon based lubricant.
Notations
- The pieces that compose the Rubik's Cube are called Cubies, and the color stickers on the Cubies are called Facelets. There are three types of Cubies :
- the centers (or center pieces), at the center of each face of the Cube. There are 6 of them, each have 1 Facelet.
- the corners (or corner pieces), at the corners of the Cube. There are 8 of them, and each have 3 Facelets.
- the edges (or edge pieces), between each pair of adjacent corners. There are 12 of them and each have 2 Facelets.
- the centers (or center pieces), at the center of each face of the Cube. There are 6 of them, each have 1 Facelet.
- Not all cubes have the same color schemes. The cube used for the illustrations is such that :
- White opposes yellow;
- Blue opposes green;
- Orange opposes red;
- Color scheme is BOY (because the Blue, Orange and Yellow faces are in clockwise order).
- White opposes yellow;
- This article uses two different views for the Cube :
- The 3D View, showing three sides of the Cube : The front (red), the top (yellow) and the right side (green). In step 4, the algorithm (1.b) is illustrated with a picture showing the left side of the cube (blue), the front (red) and top (yellow).
- The Top View, showing only the top of the cube (yellow). The front side is at the bottom (red).
- The 3D View, showing three sides of the Cube : The front (red), the top (yellow) and the right side (green). In step 4, the algorithm (1.b) is illustrated with a picture showing the left side of the cube (blue), the front (red) and top (yellow).
- For the top view, each bar indicates on which side the important facelet is located. On the picture, the yellow facelets of the top back corners are on the top (yellow) side, while the yellow facelets of the top front corners are both located on the front side of the cube.
- When a facelet is grey, it means that its color is not important for the situation considered.
- The arrows (blue or red), show what the algorithm will do. In the case of the algorithm (3.a) for instance, it will rotate the three corners on themselves as shown. If the yellow facelets are as drawn on the picture, at the end of the algorithm they will be on top.
- The axis of the rotation is the big diagonal of the cube (from one corner to the corner all the way on the other side of the cube).
- Blue arrows are used for clockwise turns (algorithm (3.a)).
- Red arrows are used for counter-clockwise turns (algorithm (3.b), symmetrical to (3.a)).
- The axis of the rotation is the big diagonal of the cube (from one corner to the corner all the way on the other side of the cube).
- For the top view, the light blue facelets indicate that an edge is incorrectly oriented. On the picture, the edges on the left and right are both incorrectly oriented. Which means that if the top face is yellow, the yellow facelets for those two edges are not on the top, but on the side.
- For the move notations, it is important to always look at the cube from the front side.
- : Rotation of the front side.
- : Rotation of one of the three vertical rows.
- : Rotation of one of the three horizontal rows.A few examples of moves : START
- : Rotation of the front side.
Related wikiHows
- How to Solve a Rubik's Cube with the Layer Method
- How to How to Solve a 2X2X2 Rubik's Cube
- How to Solve a Rubik's Cube Using Commutators
- How to Make the "H" Pattern on a Rubik's Cube
- How to Make Awesome Rubik's Cube Patterns
- How to Make a Speedcube
Sources and Citations
- Speedcubing.com - algorithms, videos, cube solvers, world records and ranking.
- Beginner Solution to the Rubik's Cube.
- Solving the cross tips and examples.
- Solution for solving the Rubik's Cube step by step illustrated method.
- Petrus Method illustrated with java animations.
- ↑ http://www.speedcubing.com/f2l.html (Algorithms > First two layers)
- ↑ http://www.speedcubing.com/finallayer.html (Algorithms > Final layer)
- ↑ http://lar5.com/cube/
Article provided by wikiHow, a wiki how-to manual. Please edit this article and find author credits at the original wikiHow article on How to Solve a Rubik's Cube (Easy Move Notation). All content on wikiHow can be shared under a Creative Commons license.
February 2, 2009
How to Make a Duct Tape Wallet
from wikiHow - The How to Manual That You Can Edit
Everybody needs a wallet, right? If you have a taste for the unconventional, or you're simply a stubborn do-it-yourselfer, then whip out that roll of duct tape and make your own wallet!
Steps
- Rip a strip of tape at least 12 inches (295 mm) in length and place it sticky side up on your working surface.
- Rip a second piece of equal length and place sticky side down halfway over the first strip. Fold the rest of the strip facing up over the second strip.
- Flip over the two strips and place a third strip sticky side down covering the remaining sticky part of the second strip. Flip the sheet again and continue extending the size of the sheet until you've created a large sheet of duct tape that is 8.5 inches (215 mm) by 7 inches (175 mm).
- Trim all the edges.
- Fold the wallet in half and tape 3 sides (bottom and two sides) to create a large pocket to hold bills.
- To create credit or business card pockets, make another sheet that's 4 by 3.5 inches (100 mm by 90 mm).
- Fold 1.5 inches (40 mm) over. To create two more pockets, repeat the step above and then tape the two pieces together, taping the second pocket a little lower on top of the first piece.
- Tape the edges of the pockets and then tape the whole piece to the large pocket. To create another pocket, leave the inside part untaped.
- Make a sheet of tape (as in the first step) larger than your ID card. Cut the sheet so that there is a 5 mm frame (big enough so you can see your picture and info, but small enough so the ID can't fall through the opening). Now trim the outside so it is slightly larger in all directions than your ID. Tape three sides of this window to the inside of your wallet, or on top of the credit card holder. It'll take a some trial and error to get it right, but it will be a great addition to the wallet. When you're done, the ID should be able to slide into the untaped side of the holder, and once in, not fall through the open window.
- Tape the completed pocket to the large pocket and again, you can create an extra pocket if you wish by leaving the inside part untaped.
- Put your money, ID, and cards in your wallet and go show off your new creation!
Tips
- Another way to make the initial square of duct tape material, you can also lay strips down slightly overlapping, sticky side up. Then, cover them with strips going the opposite way (vertical instead of horizontal or horizontal instead of vertical), slightly overlapping. This way may be more sturdy.
- There are many ways to personalize this design. Some other ideas are coin pockets within the large bill pocket and placing flaps on the credit card holders so business cards don't fall out when the wallet gets dropped.
- Use a sheet protector and cut out a piece of the clear plastic to cover the open window over your ID
- Index cards can be used to give it some structure. It also gives something for the duct tape to stick to. Of course, then it won't be made of only duct tape.
- Duct tape comes in colors too. Try out combinations, and find one you like.
- If making a clear cover for a driver's license, try using clear packing tape instead of sheet protectors if you want the entire wallet to be made out of tape.
- If cutting the duct tape with scissors, it is easier to make large cuts rather than small cuts.
- You can make a wallet latch with a little extra duct tape. Take a wide piece and fold it over to where no part is sticky. Do this again with a thinner, longer strip. Tape the bigger strip to where it will wrap all the way around the side of the wallet where you pull it open, and then the same with the thinner strip.
- You can personalize the wallet by using clear duct tape too. Use photos that you like and place them on each side and then use the clear tape to seal them in. There are endless designs you can do to make the wallet completely personal.
- If you are using a knife, a metal or metal edged ruler is best.
- Try making them out of paper, cloth, fishnet, or painter's tape (blue tape).
- Black Tyvek tape is available in 2 and 4 inch widths from book binding suppliers for a nice low key look.
- If you make the 8.5 X 7 inch duct tape sheet on aluminum foil the wallet will shield RFID credit cards.
- Put butter or margarine on your scissors to make cutting the duct tape easier.
- If you get good enough at making these you can make money selling them. A good mark-up would be $3 for a wallet. Selling at events like field trips is a good idea.
- Another good idea for personalizing your wallet would be to put stickers on it. For about $2 you can get stickers with logos on them. They are sold at most sporting goods stores.
Warnings
- Measure carefully. If anything is too small, it might not fit all of your money or cards and you'll have to start all over. Make it bigger than you think it needs to be.
- Be very careful with the blade, or use scissors!
- Try to take it nice and slow, if you have any air bubbles in it,it ruins the look.
- Don't leave your wallet in the heat or else it will get really sticky all over your money!
Things You'll Need
- Duct tape (any color of your choice)
- Ruler
- Knife or scissors
- Piece of wood or cutting board (don't use materials that will come off with duct tape)
Related wikiHows
- How to Make a Duct Tape Case for Your Ipod Nano
- How to Make a Duct Tape Book Mark
- How to Make Duct Tape Fabric
- How to Create a Packing Tape Sculpture
- How to Create a Gangster Bankroll
- How to Make a Duct Tape Purse
- How to Make an Umbrella Pouch
- How to Use Wine Bottle Labels As Art
- How to Make a Three Fold Duct Tape Wallet
- How to Hang a String of Pictures on a Wall
Sources and Citations
Article provided by wikiHow, a wiki how-to manual. Please edit this article and find author credits at the original wikiHow article on How to Make a Duct Tape Wallet. All content on wikiHow can be shared under a Creative Commons license.