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Complete F4L example for 5x5x5

Scramble. (U'BL'MUU'R'BMFFRU2MRR'RMBB'DMDD2MBB'F2DMLL2R'D2MDD2UL'D2MUU'MFF'R'MFF'LR'MDD'MBB'U2RMDD2MUU'F'LB2MBB2F'MLL'BMBB2F'MLLBD2U2L'MLL2MRRR2BMBB'LMBB'MRR2RU)







Step 1 to solve red centers







Step 2 solve all the center slice







Step 2 Solve one slice of blue.







Step 3 Solve one slice of yellow.







Step 4 Solve one slice of green.







Step 5 Solve one slice of white







Step 6 Solve second slice of white







Step 7 Solve second slice of green







Step 8 Solve second slice of yellow








Step 9 Solve second slice of blue. All center plus edges are solved now.







Step 10 Solve first corner group.







Step 11 Solve second corner group.







Step 12 Solve third corner group.







Step 13 Solve last corner group.







Step 14 Solve corners of last layer.







Step 15 Solve edges of last layer.







Step 16 First 3-cycle









Step 16 Second 3-cycle







Step 17 Last 3-cycle and solved.

Complete F3L example.

The scramble

F'ML'RML2F2LMLD'MR'U2MLMR'MDUMD2MR2D'F'MU'L'MD'MR'D'ML2R'DMF'D'LML2DMD2MF'B2DL'F2







Step 1. Match red centers.







Step 2. This is lucky so I solve two slice of Yellow.








Step 3. Solve one slice of blue.







Step 4: Solve one slice of green.







Step 5 Solve one white slice.







Step 6 Solve second green slice







Step 7 Solve another slice of blue.







Step 8. Solve the last slice







We have solved all the 8 center + edges. Now it is time to solve the corner + edges.

Step 9. Solve Red.green.white







Step 10 Solve Red.Blue.White







Step 11 Solve Red.Blue.Yelow







Step 12 Solve corners of upper layer







Step 13 Solve one white and one yellow edge using 3 cycle.







Step 14 Another 3-cycle







Step 15 Solve the 2 swap. (50% chance)

Some special 4-cycle. (II 3 cases)

Case 1






Case 2







Case 3

Some special 4-cycle. (I 3 cases)

Case 1 This is quite basic.








Tip( Add MR' and it can convert to a 2 swap)






Case 2.






Case 3

All the 2-2 swap general.

There are still some cases not listed but in general if you cannot us simple 2-2 swap use two 3-cycle.
If I find more easy 2-2 swap I will add to the existing post.

All the 2-2 swaps for 4x4x4 (IIIa, 5 Cases)

Case 1.






Case 2.
Use two 3-cycle.






Case 3.
Use two 3-cycle.






Case 4






Case 5

All the 2-2 swaps for 4x4x4 (IId,2 Cases)

Case 1






Case 2
Two 3-cycle

All the 2-2 swaps for 4x4x4 (IIc,2 Cases)

Case 1







Case 2

All the 2-2 swaps for 4x4x4 (IIb,4 Cases)

Case 1.






Case 2.






Case 3.






Case 4

All the 2-2 swaps for 4x4x4 (IIa,5 Cases)

Case 1.
Convert to Case Ic.







Case 2.






Case 3







Case 4






Case 5.

All the 2-2 swaps for 4x4x4 (Ic, 1 case)

Case 1.






Another solution.

All the 2-2 swaps for 4x4x4 (Ib, 4 cases)

Case 1.






Two 3-cycle






Case 2.






Two 3-cycle






Case 3.






Case 4

All the 2-2 swaps for 4x4x4 (Ia, 5 cases)

Case 1. (This can be used to flip two edges for 3x3x3 blind solving.







Case 2.






Use two 2-cycle. (shorter)






Case 3






Use two 3-cycle (shorter)






Case 4 (convert to case 1)






Case 5






Two 3-cycle

All the three-cycle. (III, 1 case)

There is only one case in this family.

All the three-cycle. (II, 3 cases)

Case 1.
Solution 1





Solution 2.






Case 2.
Solution 1.






Solution 2.






Case 3

All the three-cycle. (I, 4 cases)

Case 1.






Case 2.






Case 3.






Case 4. This is similar to Case3.






The other two cases in this family are just the mirror of case 1 and case 2.

All the two swap on 4x4x4 (7 cases)

The number of all the two swap on 4x4x4 is 7. I will list them all.(Case 1)







A better solution







Any second cube is not on the same side as the first one can use setup to use the case 1. (case 2)






(Case 3)





(Case 4)





Another handy way for case 4.





Case 5 is the mirror of case 2.





Case 6 is the mirror of case 3.





Case 7 is unique.

Basic 2-2 swaps.

On Rubik 4x4x4 last layer. Here is the Basic 2-2 swap.(Case 1)






Here is another basic 2-2 swap.(Case 2)







Slightly changed will be. ((Case 3)






I will make more complete list after all the 3 cycles are listed.