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There is a way of solving corners intuitively without using commutators or algorithms that hundreds of people use. (In FMC, DR/CO -> Solved Corners w/ intuition)

But, it isn't as easy on beginners. In fact, algorithms are actually the best for beginners. Memorizing 2 short 8 move algs is much, much easier for beginners than using intuition to solve corners, as they don't really know how the cube works in the same way that you do.

People have this misconception that algorithms are harder on beginners than nice intuition, but the actual fact is, it is exactly the opposite.
Ya, I can of figured while developing this it would have to be not beginner friendly. But because of what you said in the first part, It's possible to do algless/commutatorless CF.
 
Beginner's CF Method

Step 1: Orient Corners
Step 2: Permute Corners
Step 3: Solve 3 Edges On One Layer
Step 4: Solve All Edges On Opposite
Step 5: Align & Do Intuitive L5E In Some Way

0 Algorithms

I taught this way of solving edges to a real person and they understood it very quickly. I taught them layer -> CP -> CO for the corners first step though. I was surprised how fast he picked up this way of solving edges. The only difficult part was doing EO during L5E/LSE.

R2 B2 F2 D' F2 U F2 L2 U' L D2 R' B F R' D2 B U F2

(z2 y)
F R2 U R // CO
D' R2 D' R2 U R2 U' L2 U2 D // CP
F E F' u R E R' y2 U M' U' M // 3 Edges of Layer
x2 z' M U M' U' R M2 U M' U' r U M' U' r U M' U' // Full Opposite Layer
M' U M' U' M U M' // EO
U M' U2 M U M2 U' // LR
M2 U2 M' U2 M // Finish the cube
(61 moves total, 0 algorithms whatsoever)
 
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Beginner's CF Method

Step 1: Orient Corners
Step 2: Permute Corners
Step 3: Solve 3 Edges On One Layer
Step 4: Solve All Edges On Opposite
Step 5: Align & Do Intuitive L5E In Some Way

0 Algorithms

I taught this way of solving edges to a real person and they understood it very quickly. I taught them layer -> CP -> CO for the corners first step though. I was surprised how fast he picked up this way of solving edges. The only difficult part was doing EO during L5E/LSE.

R2 B2 F2 D' F2 U F2 L2 U' L D2 R' B F R' D2 B U F2

(z2 y)
F R2 U R // CO
D' R2 D' R2 U R2 U' L2 U2 D // CP
F E F' u R E R' y2 U M' U' M // 3 Edges of Layer
x2 z' M U M' U' R M2 U M' U' r U M' U' r U M' U' // Full Opposite Layer
M' U M' U' M U M' // EO
U M' U2 M U M2 U' // LR
M2 U2 M' U2 M // Finish the cube
(61 moves total, 0 algorithms whatsoever)
Wait didn't you just say that you had to use A FMC method to solve corners intuitively?
 
Anyway, here's what I came up with. No algs, but takes no CF knowledge to do, except for maybe CO and CP.
1. CO
2. CP
3. Solve BR and FR
4a. Put the BL edge in the FL place correctly oriented.
4b. Solve FL. This automatically solves BL.
5. Solve FD and BD
6. Intuitive L6E
You can put the FL edge in the BL spot and solve BL if it's more convenient. Also color neutrality isn't too hard.
These are some more details on how I solve with this.
1. Dunno how to do it
2. Dunno how to do it
3. First edge: You can insert to E slice with M and S
3. Second edge: Move edge to M slice, then use R (insert with M) R' or R' (insert with M) R, depending on it's orientation.
4a. Move to S slice and do the same idea in 3 but with R moves and the S slice.
4b. Same idea as 4a but you can't insert FL from UL.
5. Same idea as the others except E Slice and L/R moves.
6. Just do it.
This is by no means how you have to do it, just how do it.
It's really not the greatest, but at least I came up with it. @WoowyBaby if you don't mind, can you do a few example solves?
 
Anyway, here's what I came up with. No algs, but takes no CF knowledge to do, except for maybe CO and CP.
1. CO
2. CP
3. Solve BR and FR
4a. Put the BL edge in the FL place correctly oriented.
4b. Solve FL. This automatically solves BL.
5. Solve FD and BD
6. Intuitive L6E
You can put the FL edge in the BL spot and solve BL if it's more convenient. Also color neutrality isn't too hard.
These are some more details on how I solve with this.
1. Dunno how to do it
2. Dunno how to do it
3. First edge: You can insert to E slice with M and S
3. Second edge: Move edge to M slice, then use R (insert with M) R' or R' (insert with M) R, depending on it's orientation.
4a. Move to S slice and do the same idea in 3 but with R moves and the S slice.
4b. Same idea as 4a but you can't insert FL from UL.
5. Same idea as the others except E Slice and L/R moves.
6. Just do it.
This is by no means how you have to do it, just how do it.
It's really not the greatest, but at least I came up with it. @WoowyBaby if you don't mind, can you do a few example solves?

I'll do one-

Scramble: F' R D2 L2 B2 L2 U R2 D' F2 D2 R2 B2 L' U B D2 B U' B'

R' F U' F' // CO
U F2 U F2 R2 U R2 U' R2 // CP
U2 D' R' E2 R u' y' // BR+FR
L' U2 S U S' U L // BL+FL
// DL+DR
U M U' M' U' M U M // EO
U' M2 U // LR
E2 M E2 M // 4C

This scramble literally has 5 c/e pairs to start out with lmaoo. And after I solved corners I already had like 3 edges solved. But there's the example solve of your method!
 
I'll do one-

Scramble: F' R D2 L2 B2 L2 U R2 D' F2 D2 R2 B2 L' U B D2 B U' B'

R' F U' F' // CO
U F2 U F2 R2 U R2 U' R2 // CP
U2 D' R' E2 R u' y' // BR+FR
L' U2 S U S' U L // BL+FL
// DL+DR
U M U' M' U' M U M // EO
U' M2 U // LR
E2 M E2 M // 4C

This scramble literally has 5 c/e pairs to start out with lmaoo. And after I solved corners I already had like 3 edges solved. But there's the example solve of your method!
Well I guess if got nothing better to do during quarentine, do I'll learn my method. Do you know of any good CO/CP resources?
 
Well I guess if got nothing better to do during quarentine, do I'll learn my method. Do you know of any good CO/CP resources?
I would say just look at how triggers affect CO, and then work your way down through cases to a simple case, kinda like LSE EO, you work yoir way down to an arrow case. Then there are probably better things to do but it could be a good start.
 
I would say just look at how triggers affect CO, and then work your way down through cases to a simple case, kinda like LSE EO, you work yoir way down to an arrow case. Then there are probably better things to do but it could be a good start.
Thanks! I guess now that this method is actually working, I've gotta give it a name... I'll give it one later.
Could I put someone in the task of generating algorithims for 2 part PBL on a 3x3?
Isn't that just PLL, rotate, PLL?
 
Thanks! I guess now that this method is actually working, I've gotta give it a name... I'll give it one later.

Isn't that just PLL, rotate, PLL?
No, because both layers are unsolved, and I need an alg that will solve all the corners at the same time for every case, and then an alg that will solve all the edges in both layers at the same time.
 
L8C and L8E seems like a nightmare to do algs.
Keep in mind, that corners and edges are already oriented. In square 1 EP there are 100 algs, but that can have A third taken out of it because there’s no parity on 3x3.
these are the steps:

1. Solve a side but there are no regards to permutation.
2. Solve the E Layer like you would in HF.
3. Orient the opposite side with an OLL.
4. IF there aren’t to many algs, do a PBL to solve both layers at once.
4b. If there are to many algs, do one alg to permute corners and one to permute edges.

VARIATION:
1. Solve a cross with no regard to permutation.
2. Then do Pseudo F2L BUT the E layer must be solved.
The do steps 3-4 like the one above.

Technically on the variation, you don’t have to do pseudo F2l you can just pair corners with edges even if they don’t create a proper f2l pair.
 
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I think that just doing PLL z2 PLL would be decent for a 2-look PBL. I'm probably way wrong though
No it wouldn’t be, because sometimes there will be a impossible case on one side but you still don’t have parity, cuz that impossible case (or one like it) is on the other side As well.
 
No it wouldn’t be, because sometimes there will be a impossible case on one side but you still don’t have parity, cuz that impossible case (or one like it) is on the other side As well.
That would only be 48 cases for the first PLL, 21 of which are just PLL. The second face would just be PLL.

4! x 2 = 48
 
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