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The 2x2x2 "Example Solve" Game!

Scramble: R2 F2 U R' F' R2 F U R'

x z // Inspection
F // Face+twisted corner
R' U' R B R' U2 R U' R' U // T-EG-L+ (EG with twisted corner in place, left half of bottom layer needs permuting, FRD corner is twisted clockwise)

Next scramble: R2 F2 U R' F' R2 F U R'
 
Scramble: R2 F2 U R' F' R2 F U R'

x z // Inspection
F // Face+twisted corner
R' U' R B R' U2 R U' R' U // T-EG-L+ (EG with twisted corner in place, left half of bottom layer needs permuting, FRD corner is twisted clockwise)

Next scramble: R2 F2 U R' F' R2 F U R'
There should be a 2x2 method that just solves the entire cube from a 2 piece block, provided that U and D layer pieces are in their respective layers. I'm guesstimating the alg count would be ~500

anyway,

x2 y
R' U' R U' R2
U' R U R' U' R' F R F' U'

R2 F' U' R U2 F R next scramble lol (can someone try NMCLL please)
 
R2 F' U' R U2 F R next scramble lol (can someone try NMCLL please)
U' * B2 U2 // to L3C
insert at *: [U B' U', F']

final solution: B' U' F' U B U' F' U2

8 move solution

Next: R2 F' R' F2 R' U2 R2 U' R2

There should be a 2x2 method that just solves the entire cube from a 2 piece block, provided that U and D layer pieces are in their respective layers. I'm guesstimating the alg count would be ~500
That would be like TEG with two corners allowed to be twisted instead of one, so your bottom layer could have 18 different cases. With about 40 algorithms for the last layer for each of those cases (some would have 43), that would be about 720 cases. A lot of those are already known, because TCLL+, TCLL-, EG-1, and CLL are all included, but I don't think it would be very practical.
 
Next: R U F2 R F' U F2 R' U
U' L2 F2 * U2 F2 // to L3C
Insert at *: [F' U2 F, D]

Final solution: U' L2 F U2 F D F' U2 F U R2

11 moves

Using Ortega:
z // rotate
U2 R' // face
R U2 R' U' R U' R' // OLL
y' R U' R F2 R' U R' // PBL

with cancellations: z R' U' R U' R' y' R U' R F2 R' U R'

12 moves

Next: F' R2 U' R2 U R U' F2 U'
 
Two people gave new scrambles, so I did both

Next: U F2 U' F2 R2 U' R F R'
z2 // rotate
R U' R' // orient
U R2 U' F2 // separate
R2 F2 R2 U' // PBL

11 moves

Next: U2 R' U' F' U R2 F2 U' R' U2
z y // rotate
U2 R' U2 F R' U' R2 // orient/separate
D' R2 U' B2 U2 R2 U' R2 U' // PBL

Next: F2 U' R' F U2 F U R U'
 
Two people gave new scrambles, so I did both
z y // rotate
U2 R' U2 F R' U' R2 // orient/separate
D' R2 U' B2 U2 R2 U' R2 U' // PBL

Next: F2 U' R' F U2 F U R U'
The orient/separate thing is cool.

x' y//inspection
U R' F R F' //This looks promising
F R U' R' U' R U R' F' R U R' U' R' F R F' U//nevermind

3 moves cancel = 20 moves

Next: U F2 R' U F U F2 U2 R
 
Next: U' F2 R U' F' U' F2 U2 R'

I'l try an insertion :D

Skeleton: F R2 F2 R U R' U2

Final solve: F R2 F2 R U R' U2 (B L B' R2 B L' B' R2) [15 HTM... bad]

Or

F' R' F' U F /Face
y' U2 /Adjust
R U' F2 R U2 R U' F U' /EG-1

Final solve: F' R' F' U F U2 F U' L2 F U2 F U' L U' (15 HTM)

Couldn't get to 16 moves xD

Next: R U2 F' R U2 R' F2 U R
 
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