VirtualCube 3x3x3 - Learn to solve Rubik's Cube 3x3x3

Playing Instructions

Click an arrow to turn a slice of the cube. Drag on an arrow and let go to rotate cube.
Keyboard shortcuts:
← → ↑↓<>: rotate Cube by 90°.
1 to 3: Trick1 to Trick3.
Keystroke does not work
: Reset cube.
: Scramble cube.
: Solve Step by Step with explanation.
: Solve All. Click again to stop.
: Save/Restore cube state to memory in current Session.
SuperTip: To see the highlighted cubelets or facelets referenced by a term, mouseover/click/tap/touch on the term such as Trick2 or cornerT3. To make the highlight go away, click anywhere on the left page.
Start solving the cube by clicking on the arrows.
Use to watch how Computer solves the cube with detailed step by step animation.
Visual definition of terms (mouseover or click on a term):
Corners: TOPcorners, FRONTcorners
cornerT0, cornerT1, cornerT2, cornerT3, cornerF0, cornerF1, cornerF2, cornerF3, cornerD0, cornerD1, cornerD2, cornerD3, cornerR0, cornerR1, cornerR2, cornerR3
FaceCenters: faceCenters, TOPfaceCenter, LEFTfaceCenter, FRONTfaceCenter, RIGHTfaceCenter
faceT, top face
Edges: TOPedges, FRONTedges
edgeT0, edgeT1, edgeT2, edgeT3, edgeT0 edgeF0, edgeF1, edgeF2, edgeF3,

Learn the Method

There are many methods to solving the Rubik's cube. Here we solve the cube using the following steps.

Step1: Fix 4 TOPedges by fixing edgeT0 repeatedly.

After we fixed the edgeT0 (TOP-FRONT edge), we continue to fix the next bad TOP edge by rotating it to the edgeT0 location.

Step2: Fix 3 of 4 TOPcorners

A corner is fixed when it's 3 colors match the adjoining faceCenters' color. We fix 3 TOPcorners in this step, leaving remaining 5 corners to be fixed later.

Step3: Move remaining 5 corners to their correct locations.

This step requires Trick3 to swap locations of 2 corners. See Learn Trick3.

Step4: Fix 5 edges, make them good

An edge is good if it is nice and its 2-color matches the adjoining faceCenters' color. This step uses Trick1. See Learn Trick1.

Step5: Fix last 5 corners

This step requires Trick2 to flip colors of 2 corners into the correct orientations. See Learn Trick2.

You can also learn from step by step animation. See Step by Step Animation.

Learn Trick3 (← back)

Trick3 swaps locations of 2 TOP-FRONT-corners: cornerF2, cornerF1. It is used to move a corner into its correction location (where corner's 3-color matches the 3 adjoining faceCenters' colors).

A corner such as cornerT0 is in the correct location if its 3-colors are the same 3 colors as the 3 adjoining faceCenters: TOPfaceCenter, FRONTfaceCenter, RIGHTfaceCenter.

It starts with a 4-turn move (R>T<R<T>) named RightTop.
Click or
Trick3 uses RightTop as part of the trick. Click and study the turns in slow motion.
It pays to remember that Trick3 swaps 2 TOP-FRONT-corners: cornerT3, cornerT0 and flips cornerT2 corner and leaves the other 5 corners undisturbed.
Often, in order to preserve a good corner, you need to do a pre-move before doing Trick3 so that the good corner will not be changed.
Click to see how to swap cornerT3, cornerT0 without disturbing the good corner cornerT2. The pre-move results in color flip in cornerT1 preserving cornerT2.
: → →

Learn Trick2 (← back)

Trick2 swaps flip the colors of 2 FRONT-BOTTOM-corners: cornerF3, cornerF0 from BOTTOM to FRONT.

Learn Trick2. It uses (4 turns) a total of 6 times. It flips the 2 BOTTOM colors to FRONT. It goes
,
.
To see it in action, click
It looks complicated but after some practice, you intuitively count the turns as 8,1,16,1 and amazingly the fingers remember them. It is such a joy!
Learn Trick2a. It uses same RightTop a total of 6 times. It flips 2 FRONT colors to BOTTOM. To see it in action, click . For Trick2a, you count the turns as 16,1,8,1.
Often, you need to do a pre-move before doing Trick2 or Trick2a so that the 2 target corners are at BOTTOM-FRONT.
: → →
: → →

Learn Trick1(← back)

Trick1 moves 3 edges in a cyclic manner: edgeR2->edgeD3->edgeR0. It is used to move an edge to its correct location. It sends edgeR2's top face to edgeD3's bottom face.

Trick1 involves turning middle slices. Here is another way of doing Trick1 for right-handed person.
These examples require pre-move to line up the 3 intended edges before doing Trick1.
: → →
: → →
Learn Trick1a, a useful variation of Trick1.
sends top face to left face.
:
Trick1a is actually = [pre-move]+[Trick1]+[post-move] using pre-move to flip the 2-color of edgeD3. See the equivalence:
: → →

Learn from step by step animation

To gain more insights into solving the cube, take your time to study the step by step solution by using slow animation speed and repeat a step repeatedly.

Here is a learning Tip. Scramble cube (

) and save it (

Start with the same scrambled cube using "Restore from file" icon (
1
).
Try to accomplish Step1 by yourself.
For help, use to see how the computer does the next step. Then you click [UNDO], [STOP], and try to do it yourself.
Repeat from (1) every time, until Step1 is achieved.
In a similar manner, try to accomplish other steps.

Animate Moves with turns

A cube turn has the string pattern: [FRBLDT][#NM*][#slice][<>][12]

• [FRBLDT]: F(ront), R(ight), B(ack), L(eft), D(own), T(op)
• [#NM*] optional slice#: #(0,1,2),N(last),M(middle slices),*(all slices)
• [#slice] optional number of slices. e.g. T12>2.
• [<>]: turn direction left/right or downward/upward.
• [12] optional number of 90° turn: 1=90° 2=180°.
• Examples: F>, F01>2, R12<, DM>, RN<, R*>2

Select, Enter or paste a move to see the animation.

Reset
Repeat Times. Count=0
e.g. F>,R<,B>2,L<2,D>,T< F*>,R*<2

Create your own moves (e.g. F>2,T<,R*>,D<2,FM>):

Move8:	8
Move9:	9

Scramble:

Group Theory - A 5-minute Introduction

Click Reset then click 6 times. Magically, you are back to reset state called Identity.

• Any move in Rubik's Cube has a magic-number which is the number of repeats to return to the original state. The magic-number (actually known as order) of the move is 6.

• If we denote identity state by I, RightTop move by a, RightTop twice as a², 3-times as a³, etc., then
  {a,a²,a³, a⁴,a⁵,I } forms a cylic group with 6 elements,
  {a²,a⁴,a⁶=I } a subgroup of 3 elements (of order 3),
  {a³,a⁶=I} a subgroup of order 2; a³ interestingly swaps 2 pairs of corners, so to swap back, just repeat a³. Try Reset . . The order of a³ is 2.

• Fact: Any move sequence, no matter how simple or complex generates a cyclic group that has an order number.

Order of =6 which was used to generate group of order 6 above. Count=0
Order of simple = 105
Try it: click then click 105 times Or Count=0.
Order of 1-turn move = 4. ; Order of 4-turn move = 3.
Order of 26-turn move = 3. ; Order of 9-turn move = 12.
Order of 8-turn move = 3. ; Order of 12-turn move = 2.
You can type in any move (such as R>F>R<F< or RM>FM<2T>) and determine its order:
Count=0

• Fact: A cube when scrambled with 99 turns can always be restored by repeating the same 99-turn until done because we know there is a magic-number.

• Ready for Group Theory: A Non-mathematical Introduction?

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VirtualCube 3x3x3 Demo

Learn to Solve Rubik's Cube 3x3x3

Solve step by step