The title turned out really bad , anyway this is how I solved the cube intutively for the first time
The other day I decided to ignore all the algorithms I knew and to just solve the cube with out any algorithms and figure it out myself.
I found this method of solving quite easy and have achieved sub 40 times with it and I'm slow so it could get much faster.
I wouldn't say this is a speedsolving method, it's probably more of a beginners method.
I'm not very good at explaining but here it is:
Solve the edges on one side to form a cross.
Solve 3 F2L slots.
There is no particular way to do this, you could use Fridrich, LBL etc.
With the empty slot (lets say FR) it's quite easy to orientate and permute the top layer edges. Once your've solved the top layer edges
obviously the edge in the F2L slot will be automatically solved.
If you need to swap UF and UR just use R U2 R' U' R U' R' U'
Use the empty corner position in the F2L slot (lets say DFR) as a buffer and intuitively use commutators to solve the remaining 4 corners.
Again, once your've solved the top layer corners the DFR corner will automatically be solved.
If the DFR corner is already solved so you have a complete F2L, place the solved DFR corner into the top layer with something easy
(eg. R' D' R). Now your've messed up some F2L pieces, so line up an unsolved corner in the U layer into the UFR position and apply R D R'
to undo the R' D' R.
There are 3 basic sets of moves used for the corners:
You must look at the corner in the DFR position, where is the sticker that should be on the U face?
If it is on the RFD sticker/position. [apply R' D' R]
If it is on the FRD sticker/position. [apply y' R D R']
If it is on the DFR sticker/position. [apply R' D2 R D R' D' R]
Now of course this only solves orientation, so to solve the permutation just apply U, U' or U2 to set up the corner position.
Now you have to undo these moves on an unsolved corner to restore the F2L pieces.
Here's a short example of step 5:
scramble: R2 U2 R D R' U2 R D' R
Ok, the DFR corner need to go to the UFL corner.
Apply U' to set the UFL corner to UFR.
Now look at the DFR corner and where is the U face sticker? It is in the DFR sticker/position.
Apply R' D2 R D R' D' R
Now we must undo all that mess on an unsolved corner in the U layer, URB is the only one left!
Set up URB with U, and undo with R' D R D' R' D2 R.
Now here are two ways to fix these twisted corners:
-Apply some really basic commutators to flip the DFR corner counter clockwise and the UFR corner clockwise.
z' [R' D' R D R' D' R] U [R' D R D' R' D R] U z
(the "z" rotation isn't necessary at the end)
-Or you could just set the DFR corner at UFL with:
(U') R' D' R, now undo with (U) R' D R
Now we continue this normally.
FDR needs to go to UFR: y' R D R' (U') R D' R' (U)
As you can see it's not very good method, but it's pretty simple.