jazzthief81
Premium Member
Some people might remember this: https://cubezone.be/crossstudy.html
This study established that the worst case for solving the cross optimally is 8 moves regardless of the "method" you use: on a fixed color, opposite color neutral or fully color neutral.
This analysis was done with the help of the computing power of several community members since - at the time - it would have taken months to complete on the hardware of the era. We're talking single core Pentium III/Pentium 4 machines or maybe an Intel Core 2 with 2 cores if you had a relatively new machine.
Unfortunately the way the study was done, didn't allow recuperating the cube states for the absolute worst cases. It was only after the study was completed that we found out that there are 40 states with an optimal 8 move solution on each of the 6 faces of the cube.
I've been working on a full reimplementation of the code that was used to produce the results and I can now redo the whole analysis on a modern machine in a matter of days, and also with the advantage of customizing it to my needs.
So here I present the scrambles for the 40 worst possible states for the edges that are 8 move crosses on every color:
L D' R' F B U' L' D B' D2 F' L2 B2
L' U R F' B' D L U' B U2 F L2 B2
U' R' B D F U2 R' U' L F R2 D2 F B2
U2 B2 R L U' F2 U' F B' R U D' B
U' D L' D2 R F' B U' F2 D2 R' L' B
R2 B' R' L U F2 D' F B' R' U D B2
U' F B' L' U D' B D2 B R' L' U2 B2
U F' B R U' D B' D2 B' R L U2 B2
R L' D' R2 U F' B L' F2 R2 U' D' B
R2 B2 U D R' F2 R' F B' D R L' B
L2 B' R L' D F2 U' F B' L' U D B2
B L D2 R' U' D F' R L U2 B2 D B
U' F2 D2 R' L' B U' D R U2 L' F' B
R' F B' U' R L' B L2 B U' D' R2 B2
B U L2 D' R' L F' U D R2 B2 L B
D F' B L U D' B' U2 B' R L D2 B2
U' R' L B' L2 F2 U D L' B2 L' F' B
L' F' B D R2 U' R L' F' U D L2 B2
L F' B U R L' B' R2 B' U D L2 B2
L' F2 R2 U' D' B R L' U L2 D' F' B
D' F B' R' U' D B U2 B R' L' D2 B2
B L F2 L U' D' B2 L2 F R L' D B
L F B' U' R2 D R' L F U' D' L2 B2
U2 B' U' D L F2 R' F B' U' R L B2
R' L D B2 U' F' B R' U D F2 L2 B
L' F B' D' R' L B R2 B U' D' L2 B2
D2 B' U D' R F2 L' F B' D' R L B2
R' L U' L2 D F' B R' F2 L2 U' D' B
R F' B D R' L B' L2 B' U D R2 B2
U D' R' U2 L F' B D' F2 U2 R' L' B
B U F2 U R' L' B2 U2 F U' D L B
U' D R B2 L' F' B U' R L F2 D2 B
L' U' D B' D2 F2 R L D' B2 D' F' B
D' L' U B D2 R F2 L' U' R2 F B' L B2
U B R' L' D F U' L U2 R F2 L2 B
L B U' D' R F L' D L2 U F2 D2 B
U' B' R F R2 U' L' D' F R U D2 L2 B2
D R' U' F B L' D' R B' R2 F' D2 B2
D' L U F' B' R D L' B L2 F D2 B2
R' D' B L F R2 D' R' U F D2 L2 F B2
Here you can also find the same scrambles with the cross solutions for each face included: https://cubezone.be/worst_cases_color_neutral_cross_ftm.txt
This study established that the worst case for solving the cross optimally is 8 moves regardless of the "method" you use: on a fixed color, opposite color neutral or fully color neutral.
This analysis was done with the help of the computing power of several community members since - at the time - it would have taken months to complete on the hardware of the era. We're talking single core Pentium III/Pentium 4 machines or maybe an Intel Core 2 with 2 cores if you had a relatively new machine.
Unfortunately the way the study was done, didn't allow recuperating the cube states for the absolute worst cases. It was only after the study was completed that we found out that there are 40 states with an optimal 8 move solution on each of the 6 faces of the cube.
I've been working on a full reimplementation of the code that was used to produce the results and I can now redo the whole analysis on a modern machine in a matter of days, and also with the advantage of customizing it to my needs.
So here I present the scrambles for the 40 worst possible states for the edges that are 8 move crosses on every color:
L D' R' F B U' L' D B' D2 F' L2 B2
L' U R F' B' D L U' B U2 F L2 B2
U' R' B D F U2 R' U' L F R2 D2 F B2
U2 B2 R L U' F2 U' F B' R U D' B
U' D L' D2 R F' B U' F2 D2 R' L' B
R2 B' R' L U F2 D' F B' R' U D B2
U' F B' L' U D' B D2 B R' L' U2 B2
U F' B R U' D B' D2 B' R L U2 B2
R L' D' R2 U F' B L' F2 R2 U' D' B
R2 B2 U D R' F2 R' F B' D R L' B
L2 B' R L' D F2 U' F B' L' U D B2
B L D2 R' U' D F' R L U2 B2 D B
U' F2 D2 R' L' B U' D R U2 L' F' B
R' F B' U' R L' B L2 B U' D' R2 B2
B U L2 D' R' L F' U D R2 B2 L B
D F' B L U D' B' U2 B' R L D2 B2
U' R' L B' L2 F2 U D L' B2 L' F' B
L' F' B D R2 U' R L' F' U D L2 B2
L F' B U R L' B' R2 B' U D L2 B2
L' F2 R2 U' D' B R L' U L2 D' F' B
D' F B' R' U' D B U2 B R' L' D2 B2
B L F2 L U' D' B2 L2 F R L' D B
L F B' U' R2 D R' L F U' D' L2 B2
U2 B' U' D L F2 R' F B' U' R L B2
R' L D B2 U' F' B R' U D F2 L2 B
L' F B' D' R' L B R2 B U' D' L2 B2
D2 B' U D' R F2 L' F B' D' R L B2
R' L U' L2 D F' B R' F2 L2 U' D' B
R F' B D R' L B' L2 B' U D R2 B2
U D' R' U2 L F' B D' F2 U2 R' L' B
B U F2 U R' L' B2 U2 F U' D L B
U' D R B2 L' F' B U' R L F2 D2 B
L' U' D B' D2 F2 R L D' B2 D' F' B
D' L' U B D2 R F2 L' U' R2 F B' L B2
U B R' L' D F U' L U2 R F2 L2 B
L B U' D' R F L' D L2 U F2 D2 B
U' B' R F R2 U' L' D' F R U D2 L2 B2
D R' U' F B L' D' R B' R2 F' D2 B2
D' L U F' B' R D L' B L2 F D2 B2
R' D' B L F R2 D' R' U F D2 L2 F B2
Here you can also find the same scrambles with the cross solutions for each face included: https://cubezone.be/worst_cases_color_neutral_cross_ftm.txt
