Archive for August, 2007

How to solve the Rubik’s Cube

Friday, August 17th, 2007

rubikscubecross.gifA Rubik’s Cube has nine square facelets on each side, giving fifty-four facelets in total, and occupies a volume of twenty-seven unit cubes. Typically, the faces of the cube are covered by nine stickers in six solid colours; there is one colour for each side of the cube. When the puzzle is solved, each face of the cube is a solid colour. The cube celebrated its twenty-fifth anniversary in 2005, when a special edition cube in a presentation box was released, featuring a sticker in the centre of the reflective face (which replaced the white face) with a “Rubik’s Cube 1980-2005″ logo.

Solving a Rubik’s cube video

Step by Step Standard Solution

Step 0 — Notation
Before we get started, we must work out a method for describing the various moves that will be made. There are six faces, with the following notations:

  • Upper, or top face = U
  • Down, or bottom face = D
  • Left face = L
  • Right face = R
  • Front face = F
  • Back face = B

We can turn each face either clockwise or counter-clockwise, with respect to the center (i.e. a move that may be clockwise to you, when looking at the cube, may not be clockwise for that face, in relation to the middle of the cube). The names for the different kind of moves (I’ll use the U face as an example) are:

  • A 90-degree turn clockwise on a face is denoted by U.
  • A 90-degree turn counter-clockwise on a face is denoted by U’ (”U prime”) (Also note this is the same as U, done three times).
  • A 180-degree turn either clockwise or counter-clockwise on a face, is denoted by U2 (”U squared”) and is the same as two clockwise turns, or two counter-clockwise turns.

We can refer to individual pieces by a two-letter (for edges) or three-letter (for corners) combination. For example, the piece in the upper right front corner is called URF, and the edge piece to the down and left of the cube is called DL. Also, these notations refer to the piece that is in that place at that time, not the piece that should go there.

Clockwise and counter-clockwise are also used to describe orientations of corner pieces. For the URF piece, for example, rotating it clockwise would result in the U side of the piece on the R face, the R side on the F face, and the F side on the U face. Similarly, for a counter-clockwise rotation, the U side of the piece would end up on the F face, the F side on the R face and the R side on the U face.

Also, note that during any sequence of moves the position of the center pieces with respect to one another is unchanged.
Step 1 — Do the first face
I was thinking of omitting this step; if you’ve come so far as to seek help for doing the Rubik’s cube, then you’ve probably been able to do one side. But I’ve included the details in for completeness.

The first step involves choosing a color, and getting all the pieces of that color to form a complete face. These must also be in the correct relative location.

First, we will do the edges. Let’s say we pick white as the side to complete first (many people choose white as it is the easiest color to pick out). Turn the cube so that the white center piece is on the U face. Note that the centers are attached, so that they are always in the same position with respect to one another, unlike a cube of even degree (i.e. 2 x 2 x 2 or 4 x 4 x 4).

First, we put the edge pieces (those with 2 colors) in the right place. There are several possibilities. Note that when moving pieces around you should have the piece that you are working on the F face.

  • White/Other color (OC) piece is on the D face. Rotate the D face so that it is directly underneath the place where it needs to go (on the U face). If the white side of the piece is on the D face, apply F2, and it will be correct. If the white side of the piece is not on the D face, apply D R F’ R’.
  • White/OC piece is on the center slice (i.e. middle portion of the cube) . Apply F or F’ to get the piece on the D face, and then perform above moves.
  • White/OC piece is in correct position, but incorrectly rotated. Apply F2 and do the above moves as necessary.

Second, we do the corners. There are six main possibilities for each of the four corner pieces:

  • Corner piece in correct place. Do nothing.
  • Corner piece is in the correct place, but incorrectly rotated, so that the piece needs rotating clockwise. Hold the cube so that this piece is in the URF location, and apply F D F’ D’ F D F’.
  • Corner piece is in the correct place, but incorrectly rotated, so that the piece needs rotating counter-clockwise. Hold the cube so that this piece is in the URF location, and apply R’ D’ R D R’ D’ R.
  • Corner piece on D face. Rotate D face so that the corner piece you want to move into position is directly underneath its intended location. If the corner piece has white (or whatever color you chose) on the bottom, and the destination of the piece is URF (i.e. the upper right hand corner on the front of the cube), apply R’ D2 R D R’ D’ R.
  • Corner piece on D face, and white side of the corner is on the left hand side, assuming that the piece is going to the URF location. Apply F D F’.
  • Corner piece on D face, and white side of the corner is on the right hand side, assuming that the piece is going to the URF location. Apply R’ D’ R.

You should be finished the white face by now. This step is fairly intuitive, so it shouldn’t have been too much of a problem.

Step 2 — Do the middle layer edge pieces
Okay, so the U face is done…Now we have to get the edge pieces of the middle layer in place, that is the FR, FL, BR, BL pieces.

There are four possibilities:

  • Edge piece is in the correct place and oriented correctly — do nothing.
  • Edge piece is in correct place, but oriented incorrectly. In this case, you have to replace it with another piece temporarily. Choose an edge piece that is on the D face, and move it to the position of the aforementioned edge piece using the move described in the following list item.
  • Edge piece is in an incorrect place in the middle layer. In most cases, you can just skip this edge piece for now, as it will move to the D face when you put the correct edge piece in that place. If you have two edge pieces in the middle layer that are in each other’s correct places, then you will need to break the cycle by replacing one of those edge pieces with one of the D face edge pieces.
  • Edge piece is on the D face. This is good. Let’s say you want to move the yellow-red edge piece into place on the middle layer. (Your cube may not have yellow and red as adjacent pieces, so you may have to substitute different colors). Check which side of the yellow-red piece is actually on the D face. Say yellow is on the D face. Rotate the D face so that the yellow-red piece is opposite from the yellow center. (If the yellow center is on the F face, then the yellow-red piece is the DB piece, got it?). Now, hold the cube so that white is the U face, and the yellow center is on the F face. Which side of the yellow-red piece is the red face on? If the red center is on the L face, then apply F’ D’ F D L D L’. If the red center is on the R face, then apply F D F’ D’ R’ D’ R. One way to think about this move, if you’re trying to memorize it, is that you are removing the corner piece on the U side right above the edge piece you’re trying to replace, and then putting it back in from the other direction, with the side effect of moving the edge piece into the correct place.

This will have to be repeated at least 4 times in order to get all of the 4 middle layer edge pieces into place.

Step 3 — Form cross on last layer
The first two layers should now be completely correct. From now on, turn the cube upside-down, so that the first face (white, in my example) is the D face. It will remain this way until the cube is complete. The reason for this is just to make the manipulations a bit easier to perform.

On my cube, green is opposite to white, so I will refer to the green face as being the new U face for our purposes. We must now try to form a green cross, out of the green center, and the four edge pieces that surround it.

There are 4 possibilities:

  • All four pieces are correct, and you have green cross on the U face. Do nothing.
  • Two adjacent edge pieces are correct. For example, the UF and UR piece have green on the top, forming a sort of L shape, with the center. The UL and UB pieces do not have green on the top. In this situation, hold the cube so that the UF and UR pieces have green on the top (as in the example earlier in this paragraph), and apply B U L U’ L’ B’.
  • Two opposite edge pieces are correct, and the other two aren’t. Let’s say UR and UL are correct (this should make a green line down the middle of the U face). Apply B L U L’ U’ B’.
  • No edge pieces have green on the top. Hold the cube any way (still keeping the green center on the top) and apply B L U L’ U’ B’ F U R U’ R’ F’ (for those of you who want to memorize the moves, you should realize that this is the same as doing the move in the third part of this section, then rotating the cube 180 degrees, and then applying the move in the second part of this section).

You should now have the bottom two layers all correct, as before, and a green cross (or whatever the color on your cube whose center is opposite to white is) on the top face.

IMPORTANT: If the bottom two faces are perfectly correct, and you have 1 or 3 edge pieces that show green on the top, then your cube is messed up. Somebody (maybe you!) took it apart (or changed the stickers around) at some point in time. Might as well take it all apart right now, reassemble it correctly and start again.

Step 4 — Rotate U face edge pieces
You now have a green cross on the U face, but…these edge pieces may not be in the correct order. This step involves rotating them so that the can be lined up with their respective colors.

  • If all 4 pieces are correct (the entire cube is correct except for four corner pieces on the top layer), then do nothing.
  • If 1 piece is correct, then rotate the whole cube so that this piece is in the UL position (make sure green is still on the top). If the remaining 3 edge pieces need to be rotated clockwise, apply R2 D’ U2 R’ L F2 R L’ D R2. If the pieces need to be rotated counter-clockwise, apply R2 D’ R’ L F2 R L’ U2 D R2.
  • If 2 “adjacent” edge pieces (by “adjacent” here I mean pairs such as UF and UL, or UB and UL, and not UF and UB, or UR and UL), then rotate the U face so that only 1 edge piece is correct, and follow that rule.
  • If 2 opposite (i.e. not adjacent!) edge pieces are correct, then apply U or U’ and follow the rule for 0 edge pieces correct.
  • If 0 edge pieces are correct, turn the U face so that: for the UF piece (which can be any piece), the F side of that piece is the same color as the R face center. Now apply R2 D2 B2 D L2 F2 L2 F2 L2 F2 D’ B2 D2 R2.

The four U face edge pieces should now be in the correct place. The cube should be all correct now except for the four corner pieces on the U face.
Step 5 — Position U face corner pieces
Now we must move the corner pieces into the right places.

There are 3 possibilities:

  • All 4 corner pieces are in the right place, although not necessarily rotated correctly. Do nothing.
  • 1 corner piece is in the right place. Hold the cube so that it is in the UFR position. If the remaining three corner pieces need to be rotated clockwise, apply L’ U R U’ L U R’ U’. If they need to be rotated counter-clockwise, apply U R U’ L’ U R’ U’ L.
  • 0 corner pieces are in the right place. If they all need to go to opposite corners, apply R’ B2 F R F’ R’ F R F’ R’ F R F’ R’ B2 R. If they need to go to adjacent corners, hold the cube so that UFR and UFL pieces need swapping, and so do the UBR and UBL pieces. Apply B L U L’ U’ L U L’ U’ L U L’ U’ B’.

Okay, now all of the corner pieces should be in the right place. We’re almost there!
Step 6 — Rotate corner pieces
Hold the cube so that an incorrectly rotated corner piece is in the UFR position. If it needs to be rotated clockwise, apply F D F’ D’ F D F’ D’. If it needs to be rotated counter-clockwise, apply D F D’ F’ D F D’ F’. Now (and this is extremely important) turn the U face only, so that the next incorrectly rotated corner piece is in the UFR position. Apply one of the above moves, depending on which way it needs rotating. Repeat if more than two corner pieces are incorrectly rotated. After all pieces are rotated, simply turn the U face and complete the cube.

This step may be confusing, simply because after just one corner piece is rotated the cube is in quite serious disarray. Just make certain that you move only the U face and it should work out fine. I’ll give one example to show exactly what will happen, for a simple example: the UFR piece needs rotating clockwise, and the UBR piece needs rotating counter-clockwise. Do these moves and the cube will be complete F D F’ D’ F D F’ D’ U D F D’ F’ D F D’ F’ U’.

Note that there are only certain combinations of incorrectly rotated pieces. If your cube gets to a position where there is a situation other than one of these, then it has probably been taken apart by small green aliens, so I would recommend disassembling it and starting over.

  • One piece needs rotating clockwise, one piece needs rotating counter-clockwise, other two are correct.
  • Three pieces all need rotating clockwise, other one is correct.
  • Three pieces all need rotating counter-clockwise, other one is correct.
  • Two pieces need rotating clockwise, two pieces need rotating counter-clockwise.
  • I was going to write “all corner pieces are correct” here, but I guess that would be obvious.

Texts are Copyright © 1995-2007 Mark Jeays. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation.

How to make jello shots?

Thursday, August 16th, 2007

180px-bluejelloshot.jpgMaking Jello shots is like making regular Jello, except with alcohol added instead of cold water. It is poured into shot glasses or tiny cups instead of bowls.

Ingredients

  • 1 6-ounce package of gelatin (flavored or unflavored — you decide)
  • 16 ounces (2 cups) boiling water
  • 6 ounces cold water
  • 10 ounces 80-proof Alcohol (see tip for other proof liquors

Steps

  1. Assemble ingredients listed in the “Things You’ll Need” section below.
  2. In a bowl, mix boiling water with the powdered gelatin until fully dissolved. Give it at least a minute to fully activate the gelatin.
  3. Let gelatin cool for five or ten minutes to reduce alcohol vapor loss.
  4. Stir in cold water and alcohol.
  5. Pour resulting mixture into shot glasses or plastic cups
  6. Put the shot glasses or cups onto a tray and let the Jello set for two hours in the refrigerator.
  7. Dress up a party by taking Jello orange slices. Take a bunch of oranges and cut them in half. Use a spoon to cut around the edges between the rind and inner skin. Remove the fruit, leaving just the rind of half an orange. Fill the halves with Jello, and allow it to set in the refrigerator until firm. Cut the halves into thirds and you have another way of enjoying the Jello shots.

Tips

Depending on the proof of alcohol you use, adjust the proportions of alcohol to cold water to ensure that the shot still sets. Use the following ratios:
13 ounces of 30-50 (~20%) proof alcohol to 3 ounces cold water
10 ounces 80-100 (~45%) proof alcohol to 6 ounces cold water (U.S. standard)
6 ounces 150-200 proof alcohol to 10 ounces cold water

Minimize vapor loss by using a bottle of booze that was kept in your freezer for at least an hour. Be careful if you use an alcohol under 80-proof since it may freeze and break the bottle.

If you would like more “potent” shots, you can “push” the recipe a bit. This variation makes 6 large cups with 2oz (2x”shots”) of alcohol each, or 12 small cups with 1oz of alcohol each, yet still sets hard and tastes great. See warnings.

Use ice-cold alcohol. Use very hot water. Do not transfer it from the boiling vessel as this will sap critical heat. See warnings.

Dissolve 2 regular sized Jello packages or one large packet into 1.5 cups (12 oz) boiling water. Stir for at least a minute to fully dissolve and construct the gelatin.
Let cool for a few minutes - ten minutes isn’t enough to set up the Jello but it will do a lot to keep the alcohol from evaporating.

Add 1.5 cups (12 oz) of ice cold 80-proof booze of your choice (such as vodka).
Stir and pour into your cups or whatever. It sets hard in about 1 hour.Try checking your local party store for the small plastic shot cups. They also come with lids that make it really nice for serving.

Be extremely careful since these contain a lot more alcohol than you think. See warnings.
Your alcohol must be put into the freezer or dissolved. Jello must be cooled to room temperature. Failure to do so will result in the evaporation of all the alcohol before the jello sets.

Although shot glasses look prettier and allow you to see the vibrant colors of the Jello, paper cups allow for easier Jello shot consumption as they can be turned inside out. Ice cube trays also work well.

Plastic cups organize quite well in muffin trays, and are easier to handle and serve.
See the ‘how to’ on making rainbow jello for layering tips.

Be creative in mixing Jello flavors with alcohol. If you have a favorite alcoholic drink, try converting it into Jello shot form using unflavored Jello, juice, soda and alcohol.
Orange and cherry are Jello flavors that work well with Brandy.

You can match fruit flavored liquor with fruit flavored Jello. Here are some other popular liquor and Jello flavor combinations:
Lime Jello with tequila and Triple Sec (try adding a pinch of salt to the liquid mixture)
Lime Jello with Coconut Rum
Orange jello with orange cognac and brandy (such as Grand Marnier) or peach Schnapps
Unflavored gelatin with Coca Cola and rum
Cranberry Jello with vodka
Cherry Jello with cherry brandy
Raspberry jello with raspberry Schnapps
Tropical fruit Jello (or unflavored gelatin mixed with fruit punch) with dark rum or mango liqueur
Unflavored Jello with lemonade and whiskey
Strawberry Jello with light rum and strawberry liqueur (such as Pucker)
Apricot Jello with amaretto
Lime Jello with Sake
Lime Jello with Sprite, Pimm’s, and cucumber garnish
Strawberry Jello with champagne (retains some bubbles!)
Orange Jello with amaretto
Pineapple Jello with coconut rum
Blue Jello with Everclear

Warnings

Water heated in the microwave can erupt dangerously. Look for a rolling boil before opening the door. If the water does not boil after a reasonable time, do not open the door and reach in since the shock will make the superheated water erupt.

Even though Jello shots taste like candy they each contain as much or more alcohol than a beer, wine or shot, so please consume in moderation; warn your guests, wait a few minutes between shots and count your drinks.

If you are having a Jello shot party, you may want to use more water and less alcohol when making the shots to avoid destroying the guests.

Jello stains are more difficult to clean than vomit, and the latter is not as colorful as you would think.

Your needs

Small plastic cups or shot glasses, Oranges, a knife to slice them, and a spoon, stove, pot or kettle to boil water for Jello

All text above are shared under a Creative Commons License. Author: http://www.wikihow.com/Make-Jello-Shots

How do I renew Passport via Mail?

Thursday, August 16th, 2007

You should apply Passport Renewal by Mail if you..

1. Already have a passport that is not damaged; and
2. Received it within the past 15 years; and
3. Were at least age 16 when it was issued; and
4. Still have the same name as in passport (or you can legally document your name change).

If you are U.S. citizens residing abroad (except those living in Canada) should renew their passports at the nearest U.S. Embassy or U.S. Consulate. You can find your neareast US embassy in here.

For U.S. citizens residing in Canada may mail DS-82, Application for Passport by Mail, renewal applications to the address indicated on the form.  Payment must be in US dollar.

Passports renewed by mail in the U.S. may only be mailed  to U.S. and Canadian addresses.

If you mutilate or alter your U.S. passport, you may invalidate it and risk possible prosecution under the law (Section 1543 of Title 22 of the U.S. Code).

If your passport has been mutilated, altered or damaged , you cannot apply by mail. You must apply in person.

Some countries require that your passport be valid at least six months beyond the dates of your trip and/or have two to four blank visa/stamp pages.  Some airlines will not allow you to board if these requirements are not  met.

If you are behind in child support payments, you may not be able to get a passport.

Step by step renewal passport

  1. Complete Application For Passport By Mail , form DS-82. Download form here. And be sure to sign and date your application
  2. Attach mail with your most recent passport, two identical passport photographs, a $67 fee payable to the U.S. Department of State.If you need your passport urgently, you may request Expedited Service
  3. If your name has changed since your passport was issued then enclose a certified copy of the legal document specifying your name change (e.g. marriage certificate, divorce decree, adoption decree, or court order). No photocopies accepted.NOTE: If your name has changed by other means, you must apply in person.
  4. Mail in a padded envelope to:
    National Passport Processing
    P.O. Box 13349
    Philadelphia, PA 19101-3349
  5. If you use an overnight delivery service that does not deliver to a post office box, then send it to:
    National Passport Processing
    Attn: Department 13349
    1617 Brett Road
    New Castle, DE 19720

    NOTE: Include a prepaid overnight return envelope. Please note that overnight service will not speed up processing time unless the $60 fee for expedited service is also include.

For more information visit: http://travel.state.gov